Question

Match the equation on the to its equivalent in the options:
y = x^2 - 1x - 20
y = (x + 8) (x + 11)
Options:
y = x^2 + 8x + 11
y = x^2 + 19x + 88

Answer 1

To determine the equivalent form of the equation \( y = x^2 - 1x - 20 \) from the options provided, let’s first simplify the factored form.

The given factors are:

\[ y = (x + 8)(x + 11) \]

Now, we can expand this expression:

1. Multiply \( x + 8 \) by \( x + 11 \):
\[
(x + 8)(x + 11) = x^2 + 11x + 8x + 88
\]

2. Combine like terms:
\[
x^2 + 19x + 88
\]

This means that:

\[ y = (x + 8)(x + 11) \] is equivalent to

\[ y = x^2 + 19x + 88 \].

Now, we will compare with the original equation \( y = x^2 - 1x - 20 \):

To confirm if it’s equivalent, let’s try to factor \( x^2 - 1x - 20 \) to see if it results in the same factors.

To factor \( x^2 - x - 20 \):

1. We need two numbers that multiply to \(-20\) (the constant term) and add up to \(-1\) (the coefficient of \(x\)). These numbers are \( -5\) and \(4\).
2. Thus, the factorization is:
\[
y = (x - 5)(x + 4)
\]

Next, we compare:

- The expanded form of \( (x - 5)(x + 4) \) is:
\[
x^2 + 4x - 5x - 20 = x^2 - 1x - 20
\]

As we can see, this matches our original equation.

So, we conclude that:

1. \( y = x^2 + 19x + 88 \) is equivalent to \( y = (x + 8)(x + 11) \).
2. The original equation \( y = x^2 - 1x - 20 \) is a different equation.

Thus, the equivalent match from the original options given is:

**Correct option:** \( y = x^2 + 19x + 88 \).