Vertex Form of a Quadratic Function

Vertex Form of a Quadratic Function

Learning Objectives

• Determine the vertex of a quadratic function

• Graph a quadratic function in vertex form

Multiple Select

Check all of the equations that are in standard form

• $y=2x+1$

• $y=x^2+4x-9$

• $y=4\left(x-5\right)^2+3$

• $y=x^2+9$

Multiple Select

Select all equations that are in vertex form

• $y=x^2+5x$

• $y=3\left(x+4\right)^2-1$

• $y=-\left(x+3\right)^2-2$

• $y=\left(x+3\right)\left(x-2\right)$

Multiple Choice

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

• (5,-4)

• (-5,-4)

• (-15, 4)

• (15, -4)

Steps to graphing a quadratic equation in Vertex Form

• Identify the vertex (h,k)

• Select 2 more x's close to one side of the vertex to plug into the equation.

• Reflect those two points to the other side of the axis of symmetry

Poll

Did you read the previous slide?

• Yes

• No

Multiple Choice

You already have that the equation y = 3(x + 5)² - 4 has a vertex at (-5, -4). 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

• -6 and -7

• -6 and -4

• -5 and -6

• -5 and -7

Poll

If you plug in -6 and -7 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 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

Sketch the graph of the following function

 $y\ =\ 2\left(x+4\right)^2-4$  

Multiple Choice

Sketch the graph of the following function

 $y\ =\ -\left(x-3\right)^2-3$