Find a quadratic function whose graph is a parabola with $x$ - intercepts of $( - 2,0 )$ and $( 4,0 )$ and highest point $( h , 4 )$ .

Name: Find a quadratic function whose graph is a parabola with $x$ - intercepts of $( - 2,0 )$ and $( 4,0 )$ and highest point $( h , 4 )$ .
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Question

Quizplus · Accepted Answer

The Answer is In order to find

h

, find the midpoint between the points

( - 2,0 )

and

( 4,0 )

.

h = \frac { - 2 + 4 } { 2 } = 1

\Rightarrow

y = a ( x - 1 ) ^ { 2 } + 4

Since the function passes through the point

( 4,0 )

, we can find

a

by substituting these values in the equation

y = a ( x - 1 ) ^ { 2 } + 4

\Rightarrow

\alpha = - \frac { 4 } { 9 }

Thus the quadratic function is

y = f ( x ) = - \frac { 4 } { 9 } ( x - 1 ) ^ { 2 } + 4 = - \frac { 4 } { 9 } x ^ { 2 } + \frac { 8 } { 9 } x + \frac { 32 } { 9 }

.

Find a Quadratic Function Whose Graph Is a Parabola With x