Question 1

Which equation represents the general form of a quadratic function?

Accepted Answer

$$f(x) = ax^2$ + bx + c$$

Question 2

Given the quadratic function $$f(x) = 2(x + 3)^2$ - 8$$, what is the vertex of the parabola?

Accepted Answer

$$(-3, -8)$$

Question 3

For the function $$f(x) = -x^2$ + 4x + 1$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 4

If a quadratic function opens downward, which statement is true about its range?

Accepted Answer

$$(-\infty, k]$$

Question 5

What is the minimum value of $$f(x) = 4x^2$ - 16x + 1000$$ and at which $$x$$ does it occur?

Accepted Answer

Minimum value is $$984 at$$ $$x = 2$$

Question 6

A rectangle is to be enclosed with 120 feet of fencing. What is the maximum area that can be enclosed?

Accepted Answer

$$900$$ square feet

Question 7

For $$f(x) = -x^2$ + 4x + 1$$, what are the $$x-$$intercepts?

Accepted Answer

$$(2 - \sqrt{5}, 0)$$ and $$(2 + \sqrt{5}, 0)$$

Question 8

What is the domain of any unrestricted quadratic function?

Accepted Answer

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

Question 9

For $$g(x) = 2(x + 3)^2$ - 8$$, what is the minimum value and where does it occur?

Accepted Answer

Minimum value is $$-8 at$$ $$x = -3$$

Question 10

Which formula is used to find the vertex $$(h, k) of a $$quadratic in general form $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$h = -\frac{b}{2a}$$, $$k = f(h)$$

Question 11

For $$u(x) = (x - 2)^2$ + 3$$, why are there no real $$x-$$intercepts?

Accepted Answer

The minimum value is $$3$$, so $$u(x)$$ never equals $$0$$

Question 12

A student claims the vertex of $$v(x) = -(x + 4)^2$ + 7 is$$ $$(4, 7)$$ and its maximum value is $$-4. $$What is the correct vertex and maximum value?

Accepted Answer

Vertex is $$(-4, 7)$$; maximum value is $$7 at$$ $$x = -4$$

Question 13

For $$s(x) = -2x^2$ + 8x + 1$$, what is the maximum value and where does it occur?

Accepted Answer

Maximum value is $$9 at$$ $$x = 2$$

Question 14

If the leading coefficient $$a of a $$quadratic function is negative, what does this indicate about the graph?

Accepted Answer

The parabola opens downward and has a maximum

Question 15

For $$r(x) = x^2$ - 6x + 5$$, what are the $$x-$$intercepts?

Accepted Answer

$$(1, 0)$$ and $$(5, 0)$$

Question 16

Which of the following best describes the axis of symmetry for a parabola?

Accepted Answer

A vertical line passing through the vertex, $$x = h$$

Question 17

For a quadratic function with vertex $$(-2, -5)$$ that opens upward, what is its range?

Accepted Answer

$$[-5, \infty)$$

Question 18

If a quadratic function has two real zeros, what can you say about its discriminant $$D = b^2$ - 4ac$$?

Accepted Answer

$$D \u003e 0$$

Question 19

In a real-world scenario, you have 80 feet of fencing for a rectangle. What are the dimensions that maximize the area?

Accepted Answer

20 feet by 20 feet

Chapter 3 /3.1/ Quadratic Functions: Features, Graphing, and Applications

Guida di studio - Domande di pratica

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