Graphing Quadratic Functions

10.1 Graphing Quadratic Functions

Characteristics of the graph of a quadratic function.

• The graph is called a parabola. (Red graph)

• The quality of having identical parts on either side of an axis is called symmetry.

• In parabolic graphs, that line of symmetry is called the Axis of Symmetry. (Blue graph)

Fill in the Blanks

Complete the equation below for the Axis of Symmetry of this quadratic function:

$y=-2x^2-4x+2$  
x =

(type a number only)

Characteristics of the graph of a quadratic function.

• How a parabola is graphed is based on the the "a" value when the it is put in standard form.

• If a > 0 it will graph upward; if a < 0 it will graph downward.

• In the graph to the left a > 0.

Multiple Choice

Based on the function below, will it be graphed upward or downward?

$$y=x^2-4x-9$$  

• Upward

• Downward

Characteristics of the graph of a quadratic function.

• The vertex or Max (a<0) /Min (a>0) of the graph, lies on the Axis of Symmetry. On the graph at (-2,-1).

• The y-intercept is the "c" value of the function when written in standard form. On the graph at (0,3)

Multiple Choice

What are the coordinates of the vertex of this function?

$$y=x^2+4x+3$$  

• $$\left(-1,-2\right)$$  

• $$\left(-1,0\right)$$  

• $$\left(-2,-1\right)$$  

• $$\left(-3,0\right)$$  

Multiple Choice

Is the vertex of this function a maximum or minimum?
$$y=x^2+4x+3$$  

• Maximum

• Minimum

Characteristics of the graph of a quadratic function.

• A parabola also CAN have x-intercepts. These are the points on the graph that cross the x-axis.

• Green graph = 0 (zero) x-intercepts, Blue graph = 1 x-intercept, Red graph = 2 x-intercepts

Multiple Choice

How many x-intercepts does the following quadratic graph have?

$$2x^2-4x+9$$  

• Zero

• One

• Two

Multiple Choice

How many x-intercepts does the following quadratic graph have?

$$4x^2+4x+1$$  

• Zero

• One

• Two