Question

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

Explanation:

Step1: Identify x-intercepts

The x-intercepts are at \( x = -2 \) and \( x = 1 \). So, the factored form starts as \( y = a(x - (-2))(x - 1)=a(x + 2)(x - 1) \).

Step2: Find the value of \( a \)

Use the point \( (-1, 2) \) on the parabola. Substitute \( x = -1 \) and \( y = 2 \) into the equation:
\( 2 = a(-1 + 2)(-1 - 1) \)
Simplify: \( 2 = a(1)(-2) \)
\( 2 = -2a \)
Solve for \( a \): \( a = -1 \).

Step3: Write the final equation

Substitute \( a = -1 \), \( p = -2 \), and \( q = 1 \) into \( y = a(x - p)(x - q) \):
\( y = -1(x + 2)(x - 1) \) or \( y = - (x + 2)(x - 1) \).

Answer:

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