Question

write your answer in the form y = a(x - p)(x - q), where a, p, and q are integers, decimals, or simplified fractions.

Explanation:

Step1: Identify x-intercepts

The x-intercepts are at \( x = -1 \) and \( x = 3 \). So, the factored form starts as \( y = a(x - (-1))(x - 3) = a(x + 1)(x - 3) \).

Step2: Find the value of \( a \)

Use the point \( (2, 6) \) on the parabola. Substitute \( x = 2 \) and \( y = 6 \) into the equation:

$$ 6 = a(2 + 1)(2 - 3) $$

Simplify the right side: \( 6 = a(3)(-1) = -3a \).

Step3: Solve for \( a \)

Divide both sides by \( -3 \): \( a = \frac{6}{-3} = -2 \).

Step4: Write the final equation

Substitute \( a = -2 \), \( p = -1 \), and \( q = 3 \) into the factored form: \( y = -2(x + 1)(x - 3) \).

Answer:

\( y = -2(x + 1)(x - 3) \)