2. find the x -intercept about \( y=x^{2}+3 x-4 \)

To find the x-intercept of the equation \( y = x^2 + 3x - 4 \), set \( y = 0 \). This gives us the equation \( x^2 + 3x - 4 = 0 \). Using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) with \( a = 1, b = 3, c = -4 \), we find the square root discriminant to be \( b^2 - 4ac = 3^2 - 4(1)(-4) = 9 + 16 = 25 \). Plugging this into the formula yields the x-intercepts as \( x = \frac{-3 \pm 5}{2} \), giving us \( x = 1 \) and \( x = -4 \). Picture this: We're not just finding a couple of points on a graph; we’re uncovering where our quadratic curve meets the x-axis! These intercepts (1 and -4) tell you exactly where the function goes from positive to negative or vice versa. It's like the magic crossover moment of a thrilling sports match, where the ball lands just inside the line!