Final answer:
To find the values of b and c for the quadratic equation y = -13x² + bx + c with a vertex at (9,9), we use the vertex form of a quadratic equation. By substituting the given values into this form and expanding, we determine that b = 234 and c = -1044.
Step-by-step explanation:
To solve the mathematical problem completely and find the values of b and c for the quadratic equation y = -13x² + bx + c that has a vertex at (9, 9), we can use the vertex form of a quadratic equation, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Since we know the vertex is at (9, 9), we have h = 9 and k = 9, and the given “a” value is -13. Substituting these into the vertex form, we get:
y = -13(x - 9)² + 9
Expanding this, we obtain:
y = -13(x² - 18x + 81) + 9
Now, distribute the -13:
y = -13x² + 234x - 1053 + 9
Combine like terms to find the value of b and c:
y = -13x² + 234x - 1044
So, b = 234 and c = -1044.