Question 1

Given the quadratic function in standard form $$f(x) = ax^2$ + bx + c$$, what does the value of $$a$$ determine about the graph?

Accepted Answer

The direction the parabola opens and whether it is wide or narrow

Question 2

Convert the quadratic function $$f(x) = x^2$ + 4x + 2 to $$vertex form.

Accepted Answer

$$f(x) = (x + 2)^2$ - 2$$

Question 3

What is the axis of symmetry for the quadratic function $$f(x) = 2x^2$ - 8x + 3$$?

Accepted Answer

$$x = 2$$

Question 4

A projectile is fired from a cliff 300 feet above the water at an initial velocity of 400 feet per second. The height $$h of $$the projectile above the water is given by $$h(t) = -16t^2$ + 400t + 300. $$What is the maximum height reached by the projectile?

Accepted Answer

$$5300$$ feet

Question 5

Which of the following is the correct quadratic formula for finding the roots of $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 6

Find the $$x-$$intercepts of the quadratic function $$f(x) = x^2$ - 4x + 3.$$

Accepted Answer

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

Question 7

A parabolic arch has a span of 120 feet and a maximum height of 25 feet. If the vertex is at $$(0, 25)$$ and the arch touches the ground at $$x = -60$$ and $$x = 60$$, what is the equation of the parabola?

Accepted Answer

$$y = -\frac{1}{144}x^2$ + 25$$

Question 8

Given the quadratic $$f(x) = 2x^2$ - 4x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1, -1)$$

Question 9

If a quadratic function has its vertex at $$(3,1)$$ and passes through the point $$(6,-1)$$, what is its equation in vertex form?

Accepted Answer

$$y = -\frac{1}{4}(x-3)^2$ + 1$$

Question 10

Which of the following statements about the graph of $$f(x) = ax^2$ + bx + c is $$TRUE?

Accepted Answer

If $$a \u003e 0$$, the parabola opens upward.

Question 11

A ball is thrown upward from a height of 5 meters with an initial velocity of 20 m/s. Its height after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 5. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$2$$ seconds

Question 12

Which of the following is NOT a method for solving quadratic equations?

Accepted Answer

Synthetic division

Question 13

Given $$f(x) = x^2$ - 6x + 8$$, what are the solutions to $$f(x) = 0$$?

Accepted Answer

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

Question 14

The Golden Gate Bridge has two towers 4200 feet apart and 746 feet high. The cable between the towers forms a parabola. If the lowest point of the cable is 220 feet above the road, what is the height of the cable 1000 feet from the center?

Accepted Answer

$$307$$ feet

Question 15

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what does this indicate about the roots?

Accepted Answer

There are two complex (non-real) roots.

Question 16

A quadratic function models the height of a projectile: $$h(t) = -16t^2$ + 64t + 80. $$How long after launch does the projectile hit the ground?

Accepted Answer

$$t = 5$$ seconds

Question 17

Which of the following best describes the range of the function $$f(x) = -3x^2$ + 6x - 1$$?

Accepted Answer

$$(-\infty, 2]$$

Question 18

Given the quadratic $$f(x) = x^2$ + bx + c$$ has its vertex at $$(2, -3)$$, what is the value of $$b$$?

Accepted Answer

$$b = -4$$

Question 19

If a parabola opens downward and has its vertex at $$(0, 10)$$, which of the following could be its equation?

Accepted Answer

$$y = -2x^2$ + 10$$

Question 20

A quadratic function $$f(x)$$ has $$x-$$intercepts at $$x = -1$$ and $$x = 5$$, and passes through the point $$(2, -6). $$What is the equation of $$f(x)$$?

Accepted Answer

$$f(x) = -1(x + 1)(x - 5)$$

Quadratic Functions and Models: Precalculus 3.1 Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard