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# Algebra Question

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The graph of a certain quadratoc y = ax + bx + c is a parabola with vertex (-4, 0) which passes through the point (1, -75). What is the value of a?

Feb 12, 2018

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The general equation of a parabola with a vertex at  (-4, 0) is...

y   =   A(x + 4)2 + 0

We want the parabola to pass through the point  (1, -75) , so we want a value of  A  such that...

-75   =   A(1 + 4)2 + 0

-75  =  A(5)2

-75   =   A(25)

-75/25   =   A

-3  =  A

So the equation of a parabola with a vertex at  (-4, 0)  that passes through the point  (1, -75)  is...

y   =   -3(x + 4)2 + 0

y   =   -3(x + 4)(x + 4)

y   =   -3(x2 + 8x + 16)

y   =   -3x2 - 24x - 48     Here's a graph to check this:  https://www.desmos.com/calculator/ir8koxrnsi

We can see that   a = -3  .

Feb 12, 2018

#1
0

The general equation of a parabola with a vertex at  (-4, 0) is...

y   =   A(x + 4)2 + 0

We want the parabola to pass through the point  (1, -75) , so we want a value of  A  such that...

-75   =   A(1 + 4)2 + 0

-75  =  A(5)2

-75   =   A(25)

-75/25   =   A

-3  =  A

So the equation of a parabola with a vertex at  (-4, 0)  that passes through the point  (1, -75)  is...

y   =   -3(x + 4)2 + 0

y   =   -3(x + 4)(x + 4)

y   =   -3(x2 + 8x + 16)

y   =   -3x2 - 24x - 48     Here's a graph to check this:  https://www.desmos.com/calculator/ir8koxrnsi

We can see that   a = -3  .

hectictar Feb 12, 2018