Here in this question, we are to find the equation of the parabola.
Generally, the equation of a parabola is in the form;
The term (h,k) represent the coordinates of the vertex.
In this case, h = -8 and k = -7
The term 'a' is simply referred to as a multipier.
Now, we insert the coordinates of the vertex into the equation and we have the following expression;
and we have y = a(x + 8)^2 -7
To finally get the equation, we will need to calculate the value of the multiplier. The value of the multiplier can simply be calculated by substituting the value of x and y in the point through which the parabola passes.
Hence, we are substituting the values x = -7 and y = -9
So, we have;
-9 = a(-7+8)^2 -7
-9 = a(1)^2 -7
-9 = a - 7
a = -9 + 7 = -2
So our equation becomes;
y = -2(x+8)^2 - 7
we simply finish this by expanding the equation;
y = -2(x+8)(x+8) - 7
y = -2(x^2 + 16x + 64) -7
y = -2x^2 - 32x -128 -7
y = -2x^2 -32x -135
The equation of a parabola with vertex (-8, – 7) that passes through (-7, -9) is ;
