Question 1

Which of the following is the vertex form of a quadratic function?

Accepted Answer

$$f(x) = a(x - h)^2$ + k$$

Question 2

Given the quadratic function $$f(x) = -2(x - 3)^2$ + 5$$, what is the vertex of the parabola?

Accepted Answer

$$(3, 5)$$

Question 3

For the quadratic function $$f(x) = 2x^2$ - 8x + 7$$, what is the x-coordinate of the vertex?

Accepted Answer

$$x = 2$$

Question 4

A company models its profit with the function $$P(x) = -5x^2$ + 100x - 200$$, where $$x is $$the number of units sold. What is the maximum profit, and at how many units sold does it occur?

Accepted Answer

Maximum profit is $$300 at$$ $$x = 10$$ units

Question 5

Which of the following statements is true about the graph of $$f(x) = a(x - h)^2$ + k if$$ $$a \u003c 0$$?

Accepted Answer

The parabola opens downward and has a maximum at $$(h, k)$$

Question 6

Given $$f(x) = 3x^2$ - 12x + 7$$, what is the minimum value of the function?

Accepted Answer

$$-5$$

Question 7

A farmer wants to build a rectangular pen using 80 meters of fencing. What dimensions will maximize the area of the pen?

Accepted Answer

20 m by 20 m

Question 8

For the quadratic function $$f(x) = -x^2$ + 6x - 8$$, what is the range of the function?

Accepted Answer

$$(-\infty, 1]$$

Question 9

If the quadratic function $$f(x) = ax^2$ + bx + c$$ has $$a \u003e 0$$, which of the following is always true?

Accepted Answer

The function has a minimum value at its vertex

Question 10

Given $$f(x) = 2(x + 1)^2$ - 3$$, what is the y-intercept of the function?

Accepted Answer

$$-1$$

Question 11

A ball is thrown upward from the ground and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 19.6t. $$What is the maximum height reached by the ball?

Accepted Answer

$$19.6$$ meters

Question 12

Which of the following is the axis of symmetry for the quadratic function $$f(x) = 5(x - 2)^2$ + 7$$?

Accepted Answer

$$x = 2$$

Question 13

For the quadratic function $$f(x) = -3x^2$ + 12x - 7$$, what is the domain?

Accepted Answer

$$(-\infty, \infty)$$

Question 14

A rectangular garden is to be constructed using 60 meters of fencing. What is the maximum possible area of the garden?

Accepted Answer

$$225 m$^2$$

Question 15

Given $$f(x) = x^2$ - 6x + 8$$, what are the x-intercepts of the function?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 16

If a quadratic function has its vertex at $$(5, -2)$$ and opens upward, which of the following could be its equation?

Accepted Answer

$$f(x) = a(x - 5)^2$ - 2$$ with $$a \u003e 0$$

Question 17

A quadratic function models the height of a projectile: $$h(t) = -16t^2$ + 64t + 80. At $$what time does the projectile reach its maximum height?

Accepted Answer

$$t = 2$$ seconds

Question 18

Given $$f(x) = -x^2$ + 4x + 5$$, what is the maximum value of $$f(x)$$?

Accepted Answer

$$9$$

Question 19

Which of the following best describes the range of $$f(x) = 2(x - 1)^2$ + 3$$?

Accepted Answer

$$[3, \infty)$$

Question 20

If the quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(2, -5)$$ and opens downward, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, -5]$$

Quadratic Functions: Graphs, Properties, and Applications

Guida di studio - Domande di pratica

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