Question
1. find the x -intercept about \( y=x^{2}-3 x-4 \)
Ask by Ramirez Frazier. in China
Feb 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The x-intercepts are at (4, 0) and (-1, 0).
Solution
To find the x-intercepts of the graph of y = x² - 3x - 4, set y equal to 0 and solve for x:
x² - 3x - 4 = 0
This quadratic equation can be factored as:
(x - 4)(x + 1) = 0
Setting each factor equal to 0 gives:
x - 4 = 0 ⇒ x = 4
x + 1 = 0 ⇒ x = -1
So, the x-intercepts are the points (4, 0) and (-1, 0).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To find the x-intercepts of the function \( y = x^2 - 3x - 4 \), you need to set \( y \) to zero and solve for \( x \): \[ 0 = x^2 - 3x - 4 \] Factoring gives \( (x - 4)(x + 1) = 0 \), which means the x-intercepts are \( x = 4 \) and \( x = -1 \). So, the graph of the parabola crosses the x-axis at these two points! A nifty way to visualize this is by sketching the parabola. Notice that it opens upwards (since the coefficient of \( x^2 \) is positive). This means the x-axis intercepts are where your parabola dips below the axis before coming back up, making those points \( x = 4 \) and \( x = -1 \) the places where your function is just about to take off again!
