Quadratic functions-using vertex form

Quadratic functions-finding the vertex and graphing the equation when in vertex form

Objective: Students will be able to identify the vertex of an equation in vertex form and will be able to formulate a method to graph the equation

Vertex form of a quadratic equation

 $f\left(x\right)=a\left(x-h\right)^2+k$  

Vertex form KEY points

• (h, k) represents the vertex (highest or lowest point) of the parabola

• The h in ( ) represents your which is your axis of symmetry (the vertical line that divides the parabola in 2 equal halves

• The k represents your y (which is needed to complete your vertex)

• The h also represents how the far the graph shifted horizontally when x = 0

• The k also represents how far the graph shifted vertically when y = 0

Vertex form HINT when graphing

• Whatever is in ( ) is set to zero and solve for x

• If x has a coefficient of 1, your h value is the opposite of what you see

• Your k value is what you see

• Example: in the equation

    $\left(x+3\right)^2+5$  the value of h is -3 and the value of k is 5

• The vertex in the above example is (-3, 5) and shifts 3 to the right and 5 up from (0, 0)

Multiple Choice

What is the axis of symmetry of this equation?

 $f\left(x\right)=3\left(x-2\right)^2-4$  

• 3

• 2

• -4

• 4

• 2

Multiple Choice

What is the vertex of this equation?

 $f\left(x\right)=3\left(x-2\right)^2-4$  

• (2, -4)

• (-2, 4)

• (2, 4)

• (-2, -4)

Open Ended

Sketch a graph for the following equation:

 $f\left(x\right)=3\left(x-2\right)^2-4$