Final answer:
To find b and c for the quadratic equation with vertex (-8, 7), convert it to vertex form, yield y=7(x+8)^2+7. Expanding and rearranging gives y=7x^2+112x+455, hence b=112 and c=455.
Step-by-step explanation:
To find the values of b and c in the quadratic equation y=7x²+bx+c so that it has the vertex (-8, 7), we recall that the vertex form of a quadratic equation is y=a(x-h)²+k, where (h, k) is the vertex.
For this equation, since the vertex is (-8, 7) and a is 7 (from the coefficient of x²), we replace h with 8 and k with 7 in the vertex form to get y=7(x+8)²+7. Expanding the vertex form will allow us to determine the values of b and c.
Expanding y=7(x+8)²+7 gives us:
y=7(x²+16x+64)+7 = 7x²+112x+448+7
So, the quadratic equation in standard form is:
y=7x²+112x+455
Therefore, b=112 and c=455.