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

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:** \( y = (x + 3)(2x - 8) \)