Question

type the correct answer in each box. use numerals instead of words.
what is the equation of the quadratic function shown in the graph?
graph of a quadratic function
h(x) = \boxed{} (x + \boxed{})(x - \boxed{})

Explanation:

Step1: Identify x-intercepts

From the graph, the parabola crosses the x-axis at \( x = -3 \) and \( x = 1 \). So the factored form of the quadratic is \( h(x) = a(x + 3)(x - 1) \), where \( a \) is the leading coefficient.

Step2: Find the leading coefficient \( a \)

The parabola passes through the y-intercept \( (0, 6) \). Substitute \( x = 0 \) and \( y = 6 \) into the equation:
\( 6 = a(0 + 3)(0 - 1) \)
\( 6 = a(3)(-1) \)
\( 6 = -3a \)
Solve for \( a \): \( a = \frac{6}{-3} = -2 \)

Step3: Write the equation

Substitute \( a = -2 \), the roots \( -3 \) and \( 1 \) into the factored form: \( h(x) = -2(x + 3)(x - 1) \)

Answer:

\( h(x) = \boldsymbol{-2}(x + \boldsymbol{3})(x - \boldsymbol{1}) \)