Question

write an equation for a parabola with vertex at (-3, 2) that passes through (-5,3). in the form y = a(x - h)² + v fill in the values for a, h and v a= h= v=

Explanation:

Step1: Identify h and v from vertex

The vertex of the parabola is \((h, v) = (-3, 2)\), so \(h = -3\) and \(v = 2\).

Step2: Substitute vertex and point into equation

Substitute \(h = -3\), \(v = 2\), \(x = -5\), and \(y = 3\) into \(y = a(x - h)^2 + v\):
\(3 = a(-5 - (-3))^2 + 2\)
Simplify the equation:
\(3 = a(-5 + 3)^2 + 2\)
\(3 = a(-2)^2 + 2\)
\(3 = 4a + 2\)

Step3: Solve for a

Subtract 2 from both sides:
\(3 - 2 = 4a\)
\(1 = 4a\)
Divide both sides by 4:
\(a = \frac{1}{4}\)

Answer:

\(a = \frac{1}{4}\), \(h = -3\), \(v = 2\)