Quadratic Functions: Vertex, Axis, Forms flashcards

Question 1

What is a quadratic function?

Accepted Answer

A polynomial function of degree two.

Question 2

What shape is the graph of a quadratic function?

Accepted Answer

A parabola, a U-shaped curve.

Question 3

What is the vertex of a parabola?

Accepted Answer

Its extreme point (turning point): the lowest or the highest point on the graph.

Question 4

When a parabola opens up, what does its vertex represent?

Accepted Answer

The lowest point on the graph, the minimum value of the function.

Question 5

When a parabola opens down, what does its vertex represent?

Accepted Answer

The highest point on the graph, the maximum value of the function.

Question 6

What is the y-intercept of a parabola?

Accepted Answer

The point where the parabola crosses the y-axis.

Question 7

What are the x-intercepts of a parabola?

Accepted Answer

The points where it crosses the x-axis; they represent the zeros (roots) of the function, where y = 0.

Question 8

In f(x) = a(x - h)^2 + k, what point is the vertex?

Accepted Answer

(h, k).

Question 9

In general form, what does a > 0 tell you about the parabola?

Accepted Answer

It opens upward.

Question 10

In general form, what does a < 0 tell you about the parabola?

Accepted Answer

It opens downward.

Question 11

What is the axis of symmetry of f(x) = ax^2 + bx + c?

Accepted Answer

The vertical line x = -b/(2a).

Question 12

Where on the parabola does the vertex always occur, relative to the axis of symmetry?

Accepted Answer

The vertex always occurs along the axis of symmetry.

Question 13

What formula gives h, the x-coordinate of the vertex, from the general form?

Accepted Answer

h = -b/(2a).

Question 14

How do you find k, the y-coordinate of the vertex?

Accepted Answer

Evaluate the function at h: k = f(h) = f(-b/(2a)).

Question 15

What is k in f(x) = a(x - h)^2 + k, in terms of the function's output?

Accepted Answer

The output value of the function when the input is h, so f(h) = k.

Question 16

In standard form, how does k > 0 move the graph of y = x^2?

Accepted Answer

The graph shifts upward (and downward if k < 0).

Question 17

In standard form, how does h > 0 move the graph of y = x^2?

Accepted Answer

The graph shifts to the right (and to the left if h < 0).

Question 18

What is the domain of any quadratic function, unless the context restricts it?

Accepted Answer

All real numbers.

Question 19

What is the range of f(x) = a(x - h)^2 + k when a is positive?

Accepted Answer

f(x) >= k, that is, [k, infinity).

Question 20

What is the range of f(x) = a(x - h)^2 + k when a is negative?

Accepted Answer

f(x) <= k, that is, (-infinity, k].

Question 21

How do you find the y-intercept of a quadratic function f?

Accepted Answer

Evaluate f(0).

Question 22

How do you find the x-intercepts of a quadratic function f?

Accepted Answer

Solve the quadratic equation f(x) = 0.

Quadratic Functions: Vertex, Axis, Forms flashcards

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Quadratic Functions: Vertex, Axis, Forms flashcards

The cards

How this deck was checked

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