Question 1

Which of the following best describes the graph of the quadratic function $$f(x) = -2(x-3)^2$ + 5$$?

Accepted Answer

It is a parabola opening downward with vertex at $$(3, 5).$$

Question 2

Given the quadratic function $$f(x) = x^2$ - 6x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(3, -2)$$

Question 3

A ball is projected upward from a height of 100 ft with an initial velocity of 80 ft/s. Using $$s(t) = -16t^2$ + 80t + 100$$, after how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2.5$$ seconds

Question 4

Which of the following is the correct domain and range for the function $$f(x) = x^2$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[0, \infty)$$

Question 5

If the quadratic function $$f(x) = ax^2$ + bx + c$$ has $$a \u003c 0$$, which statement is true about its graph?

Accepted Answer

The parabola opens downward.

Question 6

Given the quadratic function $$f(x) = -3x^2$ - 2x + 1$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = -1$$ and $$x = \frac{1}{3}$$

Question 7

Which transformation occurs when the graph of $$f(x) = x^2$ is changed to g(x$$) = $$2(x+1)^2 - 3$?

Accepted Answer

Shifted left 1 unit, stretched vertically by 2, and shifted down 3 units.

Question 8

A hospital uses the quadratic model $$f(x) = 0.2675x^2$ + 8.186x + 537.4 to $$predict outpatient visits, where $$x is $$years since 2000. What is the predicted number of visits in 2020?

Accepted Answer

808 million

Question 9

For the quadratic function $$f(x) = x^2$ - 4x - 2$$, what is the equation of the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 10

If $$b^2 - 4ac$$ \u003c 0$$ for the quadratic equation ax^2$ + bx + c = 0$$, what can be said about the graph of $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

There are no $$x-$$intercepts.

Question 11

A ball is projected upward from a height of 100 ft with an initial velocity of 80 ft/s. For what interval of time is the ball more than 160 ft above the ground?

Accepted Answer

$$(0.92, 4.08)$$ seconds

Question 12

Which of the following is NOT a characteristic of the graph of $$f(x) = a(x-h)^2$ + k$$?

Accepted Answer

The $$y-$$intercept is always at $$k.$$

Question 13

Which of the following best describes the effect of the coefficient $$a in$$ $$f(x) = a(x-h)^2$ + k$$?

Accepted Answer

It determines the vertical stretch or shrink and the direction the parabola opens.

Question 14

If a quadratic function models the height of a projectile, what does the vertex represent in a real-world context?

Accepted Answer

The time and height at which the projectile reaches its maximum height.

Question 15

Given $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 16

Which of the following is the correct vertex formula for a quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

The vertex is at $$\left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right).$$

Question 17

Which of the following best describes the range of a quadratic function $$f(x) = a(x-h)^2$ + k$$ when $$a \u003e 0$$?

Accepted Answer

$$[k, \infty)$$

Question 18

If a quadratic regression model is used to fit real-world data, what does a positive value of $$a$$ indicate about the trend?

Accepted Answer

The data shows a U-shaped (upward opening) trend.

Question 19

A ball is projected upward from a height of 100 ft with an initial velocity of 80 ft/s. How long does it take for the ball to hit the ground?

Accepted Answer

About $$6.04$$ seconds

3-01: Study Guide: Quadratic and Polynomial Functions in Precalculus

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