QUADRATICS

Vertex Form

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Finding an equation when given the vertex



Example:

Find the equation of quadratic function that has the given vertex and given point. 

Vertex (1,3) passing through (4,8)

Vertex (1,3)= move 1 to the right and 3 up.

y=a(x-h)²+k

• Sub in the coordinates of the vertex with (h,k) being the (x,y) coordinates of the vertex. A is a multiplier which affects the steepness of the curve.

• y=a(x-1)²+3

 

• Sub in the points given on the graph (4,8)

• 8=a(4-1)²+3

• 8=a(3)²+3

• 8=9a+3

• 8-3=9a

• 5=9a

• 5/9=a

 

• Complete the equation:

• y=5/9(x-1)²+3

 

Isolating For x

On an equation in vertex form in order to find the zeroes (x-intercepts)Isolating for x is a method used. Here is a procedure on how to perform this task.

 

• o=2(x-6)2-12

Transfer the k value (-12) on the other side of the equal sign.

• 12=2(x-6)²

 

Divide each side by the a value (2)

• 12/2=2(x-6)²/2

• 6=(x-6)²

 

Square root both sides to get rid of the ²

• √6=√(x-6)²

• 2.44=x-6

 

Bring the h value over to the opposie side, solve for x

• 2.44+6=x

• 8.44=x POSSIBLE X INTERCEPT

• -2.44+6=x

• 3.56=x POSSIBLE X INTERCEPT

 

Graphing vertex form

Here is a video showing examples of graphing vertex form and give clear instructions as to perform each one.