7A Quadratic Function Features

7A: graph quadratic functions on the coordinate plane and use the graph to identify key attributes, including x-intercept, y-intercept, zeros, maximumvalue, minimumvalue, vertex, and the equation of the axis of symmetry.

​A quadratic function is one of the form
f(x) = ax² + bx + c,
where a, b, and c are numbers with a not equal to zero.

​The graph of a quadratic function is called a parabola and is u-shaped.

VERTEX : center point

​MINIMUM : the y-value of the vertex when the parabola opens up

​MAXIMUM : the y-value of the vertex when the parabola opens down

​VERTEX

​VERTEX

​MINIMUM: -4

​MAXIMUM: 0

Dropdown

A graph of a quadratic function is show on the grid.

Which coordinates best represent the vertex of the graph?

(​

Select answer

, ​

Select answer

)

Math Response

Quadratic function h can be used to model the height in feet of a rocket from the ground t seconds after it was launched. The graph of the function is shown.

What is the maximum value of the graph of the function.

Type answer here

Correct Answer: 225

Deg^°

Rad

x-intercept : also called zero, root, and solution

x-value where the parabola touches the x-axis
written as an ordered pair (x, 0)

​

Hotspot

Where are the zeros of the quadratic function graphed?

Multiple Choice

Which graph best represents a quadratic function that has only one zero?

Multiple Select

The graph of a quadratic function is shown.

Which values best represent the zeros of the function?

Select ALL that apply.

• x = 1

• x = -4

• x = -1

• x = 3

• x = -3

y-intercept : y-value where the parabola touches the y-axis
written as an ordered pair (0, y)

​(0, 1)

Multiple Choice

The graph of quadratic function r is shown on the grid.

Which answer choice best represents the intercepts of the graph of r?

• x-intercept: (5, 0)

  y-intercepts: (0, 10) and (0, -2)

• x-intercept: (0, -10) and (0, 2)

  y-intercepts: (-5, 0)

• x-intercept: (0, 5)

  y-intercepts: (10, 0) and (-2, 0)

• x-intercept: (-10, 0) and (2, 0)

  y-intercepts: (0, -5)

Axis of Symmetry (AOS) : vertical line that passes through the vertex of the parabola, making it symmetrical on both sides (split in half)
written as an equation: x = x-value of the vertex

​x = 1

Multiple Choice

Two characteristics of quadratic function p are given.

The axis of symmetry of the graph of p is x = -3.

Function p has exactly one zero.

Bases on this information, which graph could represent p?

Dropdown

The graph of a quadratic is shown on the grid. Choose from the drop-down menus to make each statement true about the parabola.

The function has ​

Select answer

zeros.

The maximum value of the function is ​

Select answer

.

The vertex of the graph of the function is ​

Select answer

.

The equation of the axis of symmetry of the graph of the function is ​

Select answer

.

Multiple Select

The graph of quadratic function k is shown on the grid.

Which statements are best supported by the graph of k?

Choose ALL that apply.

• The x-intercept is located at (-3, 0)

• The coordinates of the y-intercept are (0, 9)

• The axis of symmetry is x = -3

• The minimum is at -3

Labeling

Label the features of the quadratic function graphed on the grid.

Drag labels to their correct position on the image

vertex

axis of symmetry

y-intercept

slope

exponent

rate of change

zero

x-intercept