Question

1. given a quadratic function with a vertex at (-4, 5) and a point at (-3, 3) write the equation of the function in vertex form.

vertex form: $y = a(x - h)^2 + k$
$y = \square$

Explanation:

Step1: Identify vertex coordinates

The vertex is \((-4, 5)\), so \(h = -4\) and \(k = 5\). Substitute into vertex form: \(y = a(x - (-4))^2 + 5\) which simplifies to \(y = a(x + 4)^2 + 5\).

Step2: Substitute the point \((-3, 3)\)

Plug \(x = -3\) and \(y = 3\) into the equation: \(3 = a(-3 + 4)^2 + 5\).

Step3: Solve for \(a\)

Simplify the equation: \(3 = a(1)^2 + 5\) → \(3 = a + 5\). Subtract 5 from both sides: \(a = 3 - 5 = -2\).

Step4: Write the final equation

Substitute \(a = -2\), \(h = -4\), and \(k = 5\) back into vertex form: \(y = -2(x + 4)^2 + 5\).

Answer:

\(y = -2(x + 4)^2 + 5\)