Graphing Quadratic Equations in Standard Form

Graphing Quadratic Equations in Standard Form

ax² + bx + c = 0

Learning Targets

• 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 Blank

At what x value is the graph symmetrical? Type in a number based off the graph. x = ?

The Axis of Symmetry

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

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  $$2x^2-20x=7$$  

• x=5

• x=-5

• x= 7/2

• x=20

Fill in the Blank

Since the axis of symmetry for   $$2x^2-20x=7$$  is x = 5

Find the vertex (5, ?)

y =  

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