Question 9
8 pts

Which quadratic function, when graphed, has intercepts of 4 and -3?

Ask by Mitchell Salazar. in the United States

Jan 23,2025

Question

Question 9 8 pts Which quadratic function, when graphed, has $$ x $$ intercepts of 4 and -3? $$ y=(x+3)(2 x-8) $$ $$ y=(x-3)(x+4) $$ $$ y=(3 x-1)(x+1) $$ $$ y=(3 x+1)(8 x-2) $$

UpStudy AI · Accepted Answer

To determine which quadratic function has $$ x $$-intercepts at $$ 4 $$ and $$ -3 $$, let's analyze each option.

### Understanding $$ x $$-Intercepts
A quadratic function with $$ x $$-intercepts at $$ a $$ and $$ b $$ can be written in the factored form:
$$
y = k(x - a)(x - b)
$$
where $$ k $$ is a non-zero constant.

Given the $$ x $$-intercepts $$ 4 $$ and $$ -3 $$, the function becomes:
$$
y = k(x - 4)(x + 3)
$$
Now, let's examine each option to see which one matches this form.

### Analyzing the Options

1. **Option A: $$ y = (x + 3)(2x - 8) $$**
   $$
   y = (x + 3)(2x - 8) = 2(x + 3)(x - 4)
   $$
   This matches the desired form with $$ k = 2 $$, $$ a = 4 $$, and $$ b = -3 $$.

2. **Option B: $$ y = (x - 3)(x + 4) $$**
   - $$ x $$-intercepts: $$ 3 $$ and $$ -4 $$ (does **not** match).

3. **Option C: $$ y = (3x - 1)(x + 1) $$**
   - $$ x $$-intercepts: $$ \frac{1}{3} $$ and $$ -1 $$ (does **not** match).

4. **Option D: $$ y = (3x + 1)(8x - 2) $$**
   - $$ x $$-intercepts: $$ -\frac{1}{3} $$ and $$ \frac{1}{4} $$ (does **not** match).

### Conclusion

Only **Option A** correctly represents a quadratic function with $$ x $$-intercepts at $$ 4 $$ and $$ -3 $$.

**Answer:** $$ y = (x + 3)(2x - 8) $$
The quadratic function with $$ x $$-intercepts at 4 and -3 is $$ y = (x + 3)(2x - 8) $$.

Question 9
8 pts

Which quadratic function, when graphed, has intercepts of 4 and -3?

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Question 9 8 pts Which quadratic function, when graphed, has intercepts of 4 and -3?