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)

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