Standard Form of Quadratic Equations

Graphing Quadratic Equations in Standard Form

ax² + bx + c = 0

Learning Objectives

• Identify the Key Features of a Quadratic Function in Standard Form

• Graph a Quadratic Function in Standard Form.

Definition

A quadratic equation forms a parabola, a "U" shaped graph.

In standard form, a quadratic is of the form y= ax² + bx + c, where a, b, and c are coefficients infront of the variable x.

Fill in the Blanks

The Axis of Symmetry

The imaginary vertical line through the vertex of the parabola. The axis of symmetry divides the parabola into two symmetrical parts.
The formula for finding the axis of symmetry is:   $x=-\frac{b}{2a}$  

Multiple Choice

What is the axis of symmetry for the function

$$f\left(x\right)\ =\ 2x^2-20x-7$$  

• x= 5

• x=-5

• x= 20

• x=7/2

Vertex

Turning point of the quadratic. The highest or lowest point. Use   $x=-\frac{b}{2a}$  to find h (the x-value of the vertex). Then plug in that x-value into the function and solve for y.

Multiple Choice

What is the vertex of the function

$$y=-2x^2+4x+3$$  

• (0,3)

• (-1,5)

• (1,5)

• (1,-5)

Multiple Select

What are the x - intercepts of the quadratic shown?

• (2,0)

• (0,2)

• (0,6)

• (6,0)

Poll

Did you read the previous slide? Be Honest

• Yes

• No

Multiple Choice

Is the equation in standard form? If not, what should you do to get it in standard form?  $$2x^2\ -20x=7$$  

• Yes it is in standard form

• No, move the 20x to the other side

• No, move the 7 to the other side

• I don't know what standard form is.

Multiple Choice

What is the axis of symmetry for  $$2x^2-20x=7$$  

Hint: use  $$x=\frac{-b}{2a}$$  

• x=5

• x=-5

• x= 7/2

• x=20

Multiple Choice

This is what you should have found so far. Click on the image to enlarge. The next step is to pick 2 x’s close to the axis of symmetry and on the same side of the axis of symmetry. What would you pick? The axis of symmetry is x = 5

• 4 and 6

• 5 and 6

• 3 and 4

• 10 and 20

Poll

If you plug in 3 & 4 for x you’ll get the two points which are now graphed. When a graph has an axis of symmetry, it means the graph is the same on both sides. Do you see that you could reflect the new points across the axis of symmetry to get two more points on the other side? Click on image to make it larger.

• Yes

• No

Open Ended

Here’s what your graph should look like. What questions do you have? Click on the image to view the graph.

Multiple Choice

Click on image to enlarg

• A

• B

• C

• D