11. factor
3x² + 13x - 10
12. factor. 9m² - 16
a. (3m - 4)(3m - 2)
b. (3m - 8)(3m + 2)
c. (3m - 4)(3m + 4)
d. (3m - 4)(3m - 4)
13. solve the quadratic equation: x² - 4x + 4 = 0
14. find the exact solutions to x² - 3x + 1 = 0 by using the quadratic formula.
a. $\frac{-3 \pm \sqrt{5}}{2}$
b. $\frac{3 \pm \sqrt{13}}{2}$
c. $\frac{-3 \pm \sqrt{13}}{2}$
d. $\frac{3 \pm \sqrt{5}}{2}$
15. solve the equation.
21x² - 7x = 0
16. what is the y-intercept of the quadratic equation y = 3x² + 2x - 5 ?
a. (3,2)
b. (0,-5)
c. (0,5)
d. (-3,-2)
17. what are the x-intercepts of the graph of -x² + 3x - 2 = y?
a. x = -1, x = -2
b. x = 1, x = 2
c. x = 1, x = -2
d. x = -1, x = 2

Question

Accepted Answer

### Question 12: Factor $9m^2 - 16$
# Explanation:
## Step 1: Recognize the difference of squares
The expression $9m^2 - 16$ is a difference of squares, which follows the form $a^2 - b^2=(a - b)(a + b)$. Here, $a = 3m$ (since $(3m)^2=9m^2$) and $b = 4$ (since $4^2 = 16$).
## Step 2: Apply the difference of squares formula
Using the formula $a^2 - b^2=(a - b)(a + b)$ with $a = 3m$ and $b = 4$, we get $(3m - 4)(3m + 4)$.
# Answer:
c. $(3m - 4)(3m + 4)$

### Question 13: Solve the quadratic equation $x^2-4x + 4 = 0$
# Explanation:
## Step 1: Recognize the perfect square trinomial
The quadratic $x^2-4x + 4$ is a perfect square trinomial of the form $a^2-2ab + b^2=(a - b)^2$. Here, $a=x$ and $b = 2$ (since $2ab=2\times x\times2 = 4x$).
## Step 2: Factor the perfect square trinomial
So, $x^2-4x + 4=(x - 2)^2$. The equation becomes $(x - 2)^2=0$.
## Step 3: Solve for $x$
Taking the square root of both sides, we have $x - 2=0$, so $x=2$ (with multiplicity 2).
# Answer:
$x = 2$ (double root)

### Question 14: Find the exact solutions to $x^2-3x + 1=0$ using the Quadratic Formula
# Explanation:
## Step 1: Recall the Quadratic Formula
The Quadratic Formula for a quadratic equation $ax^2+bx + c = 0$ is $x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$.
## Step 2: Identify $a$, $b$, and $c$
For the equation $x^2-3x + 1=0$, we have $a = 1$, $b=-3$, and $c = 1$.
## Step 3: Substitute into the Quadratic Formula
Substitute $a = 1$, $b=-3$, and $c = 1$ into the formula:
$$
\begin{align*}
x&=\frac{-(-3)\pm\sqrt{(-3)^2-4\times1\times1}}{2\times1}\
&=\frac{3\pm\sqrt{9 - 4}}{2}\
&=\frac{3\pm\sqrt{5}}{2}
\end{align*}
$$
# Answer:
d. $\frac{3\pm\sqrt{5}}{2}$

### Question 15: Solve the equation $21x^2-7x = 0$
# Explanation:
## Step 1: Factor out the greatest common factor (GCF)
The GCF of $21x^2$ and $-7x$ is $7x$. Factoring out $7x$, we get $7x(3x - 1)=0$.
## Step 2: Set each factor equal to zero
Using the zero - product property (if $ab = 0$, then $a = 0$ or $b = 0$):
- For $7x=0$, we have $x = 0$.
- For $3x - 1=0$, add 1 to both sides: $3x=1$, then divide by 3: $x=\frac{1}{3}$.
# Answer:
$x = 0$ or $x=\frac{1}{3}$

### Question 16: What is the $y$-intercept of the quadratic equation $y = 3x^2+2x - 5$?
# Explanation:
## Step 1: Recall the definition of $y$-intercept
The $y$-intercept of a function $y = f(x)$ is the value of $y$ when $x = 0$.
## Step 2: Substitute $x = 0$ into the equation
Substitute $x = 0$ into $y = 3x^2+2x - 5$:
$y=3(0)^2+2(0)-5=-5$. So the $y$-intercept is the point $(0,-5)$.
# Answer:
b. $(0,-5)$

### Question 17: What are the $x$-intercepts of the graph of $-x^2+3x - 2=y$?
# Explanation:
## Step 1: Find $x$-intercepts (set $y = 0$)
Set $y = 0$, so the equation becomes $-x^2+3x - 2=0$. Multiply both sides by $- 1$ to get $x^2-3x + 2=0$.
## Step 2: Factor the quadratic
Factor $x^2-3x + 2$. We need two numbers that multiply to 2 and add to - 3. The numbers are - 1 and - 2. So, $x^2-3x + 2=(x - 1)(x - 2)$.
## Step 3: Solve for $x$
Set each factor equal to zero: $x - 1=0$ gives $x = 1$ and $x - 2=0$ gives $x = 2$.
# Answer:
b. $x = 1$, $x = 2$

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QUESTION IMAGE

Question

Explanation:

Question 12: Factor \(9m^2 - 16\)

Step 1: Recognize the difference of squares

Step 2: Apply the difference of squares formula

Step 1: Recognize the perfect square trinomial

Step 2: Factor the perfect square trinomial

Step 3: Solve for \(x\)

Step 1: Recall the Quadratic Formula

Step 2: Identify \(a\), \(b\), and \(c\)

Step 3: Substitute into the Quadratic Formula

Answer:

Question 13: Solve the quadratic equation \(x^2-4x + 4 = 0\)