Question

1. which expressions are equivalent to $x^2 + 4x - 12$?

select two answer choices.
a. $(x+2)(x+6)$
b. $(x+6)(x-2)$
c. $(x+4)(x-12)$
d. $(x+2)^2 - 16$
e. $(x+2)^2 + 16$
objective:a-sse.3a choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* a. factor a quadratic expression to reveal the zeros of the function it defines.

1. what are the zeros of the function $f(x) = 4x^2 - 25$?

select two answer choices.
a. -5
b. -2.5
c. 0
d. 2.5
e. 5

Explanation:

Problem 4 (Equivalent Expressions for \(x^2 + 4x - 12\))

Step 1: Analyze Option A

Expand \((x + 2)(x + 6)\):
\((x + 2)(x + 6) = x^2 + 6x + 2x + 12 = x^2 + 8x + 12\).
Not equivalent to \(x^2 + 4x - 12\).

Step 2: Analyze Option B

Expand \((x + 6)(x - 2)\):
\((x + 6)(x - 2) = x^2 - 2x + 6x - 12 = x^2 + 4x - 12\).
Equivalent to the given expression.

Step 3: Analyze Option C

Expand \((x + 4)(x - 12)\):
\((x + 4)(x - 12) = x^2 - 12x + 4x - 48 = x^2 - 8x - 48\).
Not equivalent.

Step 4: Analyze Option D

Expand \((x + 2)^2 - 16\):
\((x + 2)^2 = x^2 + 4x + 4\), so \((x + 2)^2 - 16 = x^2 + 4x + 4 - 16 = x^2 + 4x - 12\).
Equivalent to the given expression.

Step 5: Analyze Option E

Expand \((x + 2)^2 + 16\):
\((x + 2)^2 + 16 = x^2 + 4x + 4 + 16 = x^2 + 4x + 20\).
Not equivalent.

Problem 1 (Zeros of \(f(x) = 4x^2 - 25\))

Step 1: Set \(f(x) = 0\)

\(4x^2 - 25 = 0\).

Step 2: Solve for \(x\)

Rewrite as a difference of squares: \( (2x)^2 - 5^2 = 0 \).
Factor: \( (2x - 5)(2x + 5) = 0 \).

Step 3: Find roots

• For \(2x - 5 = 0\): \(2x = 5 \implies x = \frac{5}{2} = 2.5\).
• For \(2x + 5 = 0\): \(2x = -5 \implies x = -\frac{5}{2} = -2.5\).

Answer:

s:

Problem 4:

B. \((x + 6)(x - 2)\), D. \((x + 2)^2 - 16\)

Problem 1:

B. \(-2.5\), D. \(2.5\)