3. find the x -intercept about \( y=x^{2}-3 x-10 \)

To find the x-intercepts of the equation \( y = x^{2} - 3x - 10 \), you set \( y \) to 0, yielding the equation \( 0 = x^{2} - 3x - 10 \). Now, you can factor this quadratic equation, looking for two numbers that multiply to -10 and add to -3. Those numbers are -5 and 2, so it factors to \( (x - 5)(x + 2) = 0 \). Thus, your x-intercepts are \( x = 5 \) and \( x = -2 \)! Plotting the curve is also a blast! Sketch the parabolic shape of the function, and mark those intercepts on the x-axis. You’ll see how the graph dips down and then rises again, beautifully capturing the essence of quadratic functions. Don't hesitate to grab a graphing calculator or software to visualize these intersection points and see the full picture of the function!