Question

write the equation of the parabola that passes through the points shown in the table.

x	y
-7	0
8	15
9	0

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 roots from table

When \( y = 0 \), \( x=-7 \) and \( x = 9 \). So the factored form \( y=a(x - p)(x - q) \) has \( p=-7 \), \( q = 9 \) (or vice - versa). So the equation is \( y=a(x + 7)(x - 9) \).

Step2: Find the value of \( a \)

We know the parabola passes through \( (8,15) \). Substitute \( x = 8 \) and \( y=15 \) into \( y=a(x + 7)(x - 9) \):

$$
LATEXBLOCK0
$$

Step3: Write the final equation

Substitute \( a=-1 \), \( p = - 7 \), \( q=9 \) into \( y=a(x - p)(x - q) \), we get \( y=-1(x + 7)(x - 9) \) or \( y=-(x + 7)(x - 9) \)

Answer:

\( y =-(x + 7)(x - 9) \)