Question 1117778
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a. With vertex (-4,9) and y the dependent variable, the equation is<br>
{{{y-9 = a(x+4)^2}}}<br>
Plug in the x and y values of the given point to determine the value of the constant a.<br>
{{{25-9 = a(0+4)^2}}}
{{{16 = 16a}}}
{{{a = 1}}}<br>
The equation is<br>
{{{y-9 = (x+4)^2}}}  or  {{{y = (x+4)^2+9}}}<br>
b. Use the same strategy.<br>
Vertex (-2,9), so the equation is {{{y-9=a(x+2)^2}}}.<br>
Plug in (x,y)=(-5,0) to determine the value of a.<br>
{{{0-9 = a(-5+2)^2}}}
{{{-9 = 9a}}}
{{{a = -1}}}<br>
Equation: {{{y-9 = -(x+2)^2}}}  or  {{{y = -(x+2)^2+9}}}