Quadratic equations Questions and Answers

Select the correct labeling of a, b, and c to the standard form of the quadratic equation. a = 4, b = -2, and c = 7 4x² + 5x - 2 = 0 x² + 2x-5 = 0 x²-5=0 4x² - 2x +7=0 x² + 2x = 0

What are the solutions to 2(x-7)² = 32? A x = 7 ± √32 B x=± √65 X= C x = 3 and x = 11 D x = -1 and x = 15

Consider the following quadratic function. g(x)=2x²-16x+37 (a) Write the equation in the form g (x)= a (x-h)²+k. Then give the vertex of its graph. Writing in the form specified: g(x) = Vertex: (b) Graph the function. To do this, plot five points on the graph of the function: the vertex, two points to the left of the ver vertex. Then click on the graph-a-function button.

For the polynomial below, -3 is a zero. g(x)=x³ + 5x² + 16x + 30 Express g (x) as a product of linear factors. g(x) = 0

Using the axis of symmetry formula, find the axis of symmetry and vertex for each equation. 3. y=-x² +10x-26 4. y=3x² - 6x 5. y=2x² - 4

If the roots of the equation x² - 6x = 27 are p and t, and if t < p, then p = 1/t t2 2t -t t+6

Solve the equation by factoring. 9x² +21x-8=0

Compute the discriminant. Then determine the number and type of solutions of the given equation. x^2-4x-6=0 What is the discriminant? (Simplify your answer.) Choose the sentence that describes the number and type of solutions of the quadratic equation. A. There are two imaginary solutions. B. There are two unequal real solutions. C. There is one real solution. D. There are an infinite number of real solutions.

Solve the equation by factoring. x² = 6x +27 Rewrite the equation in factored form. (x+3)(x-9) = 0 (Factor completely.) The solution set is

Solve the quadratic equation using the square root property. (x-7)² = -3 The solution set is (Simplify your answer. Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

Solve the quadratic equation by completing the square x² +6x+4=0. To complete the square, what number should be added to both sides of the equation?

Solve the quadratic equation by completing the square. x² - 10x+12=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas. Form: Solution:

If using the method of completing the square to solve the quadratic equation x² + 8x + 37 = 0, which number would have to be added to "complete the square"?

Andrea simplified a polynomial expression. The solution was 4x²-7x + 5. Which of the following could have been the original expressions? SELECT ALL THAT APPLY. (3x²-9x+8)+(x²+2x-3) (2x² - 4x-5)-(-2x² + 3x - 10) (5x²-2)-(x²+7x+3) (4x² + 3x) -(10x + 5)

The polynomial function g is defined by g(x)=-x-5x³-4x² + 4x-1. Use the ALEKS graphing calculator to find all the points (x, g(x)) where there is a local maximum.

Solve the quadratic equation using the square root property. (x-5)² = -3

x2+5 – 2 When trying to factor, Sarita says this polynomial is PRIME. Why is she correct? there are no numbers with a product of -2, and a sum of 5 there are no numbers with a product 5, and a sum of -2 both 5 and -2 are prime numbers

Solve the quadratic equation by completing the square. x² +8x+14=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas. Form:

Which of the following is an attribute of any quadratic function? It has a constant rate of change. The function values increase as x increases. It is symmetric about a line through its vertex. The graph always intersects the x-axis twice.

A paper airplane is thrown from a height of 9 feet. The function y = -2x² + 3x +9 represents the path of the plane, where x is the distance traveled and H(x) is the height of the plane. At what distance does the plane hit the ground? 18 ft 3 ft 2 ft 9 ft

The height in feet of a ball thrown in the air from a ledge 112 feet high is represented by the function f(x) = -16x²+96x +112, where x is the number of seconds since the ball has been thrown. How many seconds does it take the ball to reach the ground? 256 7 3 112

Carter found the discriminant of this quadratic function. F(x)=6x²-5x +3 According to the discriminant, which best describes the roots of F(x)? One real root Two real roots Two complex roots One complex root

Put the quadratic into vertex form and state the coordinates of the vertex. y = x² − 6x + 8 Vertex Form: y = Vertex:

Which equation has the same solution as x² + 18x - 20 = -2? (x-9)² = 99 (x + 9)² = -63 ○ (x + 9)² = 99 (x - 9)² = -63

Alton and Eithan are each saving money for a car. The total amount of money Alton will save is given by the function f (x) = = 43 + 3x. The total amount of money Eithan will save is given by the functiong (x) = x² + 25. After how many weeks, x, will they have the same amount of money saved? Explain how you arrived at your answer.

Solve the equation below by completing the square and then solving for x. 2x²-28x-2=-50 A. x= 2 or x = -18 B. x = 7 or x = 4 C. x = 2 or x = 12 D. x = -7 or x = 4

The polynomial given below has___root(s). 3x²-8x+4 A. two positive B. two complex C. two negative D. one positive and one negative

What number would you add to complete the square for the equation below? x² + 6x = 0

Which of the following are solutions to the equation below? Check all that apply. x² + 10x + 25 = 8 A. x = 2√2-5 B. x = √17-10 C. x = -2-√√2-5 D. x = 8 + √√5 E. x = 8 - √5 F. x = -√17-10

A child launches a toy rocket in the air, and the function f(x) = -10x² +90x+ 20 represents the flight of the rocket, where x is the time in seconds and f(x) is the height (in feet) at x seconds. a. For how many seconds is the rocket higher than 100 feet above the ground? b. Explain how you found your answer.

Find the sum: (x³ + 3x²+x+1)+ (2x³ - 2x² - 2x+2). A. x³ +5x²+3x+2 B. -x³ +5x²-x+3 C. 3x³ + x²-x+3 D. 3x³ + 5x²-x+3

What number must you add to the polynomial below to complete the square? x²-26x

Find the discriminant of the following equation. x²+2x+7=0

6/x= 2x+4/5 Multiply each side by the common denominator to find the quadratic equation equivalent to this equation. A. x² + 4x-15 = 0 B. 2x² + 4x-30 = 0 C. x² + 4x-30 = 0 D. 2x² + 4x + 15 = 0

Enter the degree of the polynomial below: 2x^4 + x^9 + 5x^6 + 5x^5-7x³

What number would you add to the equation below to complete the square? x^2+3x=0 A. 3/2 B. 9/4 C. 9 D. 6

The ________ is the name of the number under the radical symbol in the quadratic formula.

What number must you add to complete the square? x^2 +12x=9

Find the product and enter it in the box below. Enter your answer as a polynomial in descending order and use the caret (^) for exponents. For example, you would write 4x2 as 4x^2. (5x+1)(5x+8)

Find all ordered pair solution (s) to the system of nonlinear equations given by: y=-x-5 y = x² - 5 If there is more than one solution, enter as a list of ordered pairs. Example: (2,-5), (5,-2)

Given the following quadratic equation, state the x and y intercepts (solutions of the form (x, 0) and (0, y)), the vertex, and then use this information to sketch the graph: a) y = x² - 2x-3 b) y = x² + 2x c) y = -x² + 4x-2

The points (0, 2), (1, 3), (2, 6), and (3, 11) are on the graph of a function. Which of the following equations represents that function? A h(x) = 0.5x² +1.5 B. h(x) = x² + 2 C. h(x) = x + 2 D. h(x) = 2x²

A ball was thrown upward into the air. The height, in feet, of the ball above the ground t seconds after being thrown can be determined by the expression -16t^2 + 40t + 3. What is the meaning of the 3 in the expression? A. The ball was thrown from a height of 3 feet. B. The ball took 3 seconds to reach the ground. C. The ball reached a maximum height of 3 feet. D. The ball took 3 seconds to reach its maximum height.

Determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function. The ƒ(x) = x² + 4x − 1

Write the quadratic function in the form g(x)= a (x −h)² + k. Then, give the vertex of its graph. g(x)=x² + 4x +3

Find all real solutions of the equation (9x + 2)² = 36. Write your answers as a list of integers or reduced fractions in the form A/B. For example, if your answers are 2/3 and 5, you would enter 2/3,5

Find all real solutions of equation 4x² + 5x - 4 = 0. Does the equation have real solutions? Input Yes or No: If your answer is Yes, input the solutions:

Find all real solutions of the equation 4k² + 15 = 271.

Consider the parabola given by the equation: Find the following for this parabola: y = x² + 6x - 8 A) The vertex = B) The y intercept is the point (0, C) Find the two values of that correspond to the x intercepts of the parabola and write them as a list, separated by commas: x = Round your answer(s) to two decimal places.

Consider the parabola given by the equation: f(x)=x²-12x + 13 Find the following for this parabola: A) The value of f(-5): B) The vertex = C) The y intercept is the point (0, D) Find the two values of a that make f(x) = 0. Round your answers to two decimal places. Write the values as a list, separated by commas: