# Quadratic equations Questions and Answers

Math

Quadratic equationsYou throw a baseball upward with an initial velocity of 56 feet per second. The height h (in feet) of the baseball relative to your glove is modeled by the position function h(t)= -16t2+56t where t is the time in seconds. How long does it take for the ball to reach your glove? (Round your answer to one decimal place.)

Math

Quadratic equationsYou are working with the following quadratic function: y = x² - 2x - 8
a) Write the quadratic in factored form: y=
b) Complete the square to write the quadratic in vertex form: y =
Identify the vertex of the parabola:
Remember that the vertex is a point!
Identify the y-intercept of the parabola:
Remember that the y-intercept is a point!
Identify the x-intercepts: and
Remember that the x-intercepts represent points on the graph!

Math

Quadratic equationsThis question is not about solving the stated problem, but about understanding it.
A rocket is launched, and its height above sea level t seconds after launch is given by the equation h(t) = 4.9t² + 1300t + 170.
a) From what height was the rocket launched?
b) What is the maximum height the rocket reaches?
c) If the rocket will splash down in the ocean, when will it splash down?

Math

Quadratic equationsUse the discriminant to determine whether the quadratic equation has zero, one, or two distinct real solutions.
x² + 6x + 1 = 0
The quadratic equation has choose one real
solution(s).

Math

Quadratic equationsIs it more convenient to complete the square for x^2 + bx when bis odd or when b is even? Explain.

Math

Quadratic equationsSolve the following quadratic expressions by factoring. First write the expressions in completely factored form. Then write the real number solutions. [Hint: Remember to use proper notation when writing the real number solutions. For example: if the solutions are a = 1 and x = 4, write x 1,4

Math

Quadratic equationsA jazz group on tour has been drawing average crowds of 1000 people. It is projected that for every $1 increase in the $17 ticket price, the average attendance will decrease by 60. What equation could be used to solve this problem and at what ticket price will nightly receipts be $16,400?
A) (17+x)(1000-60x)=16400;
$20
B) (17x)(1000x-60)=16400;
$20
C) (17+x)(1000-60x)=16400;
$19
D) (17-x)(1000+60x)=16400;

Math

Quadratic equationsFactorize (144z2y² - 225a²b²).
(12zy - 15ab)²
(12zy-15ab)(12zy + 15ab)
(12zy + 15ab)²

Math

Quadratic equations3. Find the zeros of the quadratic function by graphing. Round to the nearest tenth if necessary.
f(x) = -2x² + 3x + 1
0.8,2.1) is a zero of the quadratic function because it is the peak of the parabola.
(-0.3,0) and (1.8,0) are zeros of the quadratic function because it is where the parabola crosses the x-axis.
(0.8,2.1) and (0,1) are zeros of the quadratic function because it is where the parabola crosses the x-axis...
(0.1) is a zero of the quadratic because it is where the parabola crosses the y-axis.

Math

Quadratic equationsWhich of the following reveals the minimum value for the equation 3x2 + 18x+15=0?
3(x+3)² = 6
3(x+9)² = 12
3(x+3)² = 12
3(x+9)² = 228

Math

Quadratic equationsConsider the parabola given by the equation:
y = 1x² + 14x - 33
Find the following for this parabola:
A) The vertex = (
B) The y intercept is the point (0,
C) Find the two values of a that correspond to the intercepts of the parabola and write them as a list, separated by commas:

Math

Quadratic equationsA person standing close to the edge on top of a 112-foot building throws a ball vertically upward. The quadratic function h(t)=16t² +96t+ 112 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.
a) What is the maximum height of the ball?
b) How many seconds does it take until the ball hits the ground?

Math

Quadratic equationsFind all real solutions of the equation
(b + 3)² = 294
After simplifying, the solutions should look like b = A +- B√C where
A =
B =
C =

Math

Quadratic equationsNASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = -4.9t² +241t+ 178. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak?

Math

Quadratic equationsAn object is thrown upward at a speed of 132 feet per second by a machine from a height of 17 feet
off the ground. The height of the object after t seconds can be found using the equation
s(t) = 16t² + vot + so, where is the initial velocity and so is the initial height. Give all
numerical answers to 2 decimal places.
(a) When will the object reach its maximum height?
(b) What is its maximum height?
(c) When will the object reach the ground?

Math

Quadratic equationsSolve this equation using the square root property. If possible, simplify radicals. All answers should be exact.
(c - 9)² = 29
The solution(s) to this equation have the form c = A ± √B