Question

1. a quadratic function has a vertex at \\((9, -3)\\) and passes through \\((4, 97)\\).

Explanation:

Write the vertex form equation

Using the Quadratic Vertex Form knowledge point

$$ y = a(x - h)^2 + k $$

$$ (h, k) = (9, -3) $$

$$ y = a(x - 9)^2 - 3 $$

Substitute the given point to solve for a

Using the Determining Quadratic Equations knowledge point

$$ (x, y) = (4, 97) $$

$$ 97 = a(4 - 9)^2 - 3 $$

$$ 97 = a(-5)^2 - 3 $$

$$ 97 = 25a - 3 $$

$$ 100 = 25a $$

$$ a = 4 $$

Write the final quadratic equation

Using the Determining Quadratic Equations knowledge point

$$ y = 4(x - 9)^2 - 3 $$

Answer:

\(y = 4(x - 9)^2 - 3\)