Question

The instructions say to use foil or a generic rectangle and find the x-intercepts. Then sketch the parabola for the following equations:

1) y = x²- 2x - 15
2) y = x²+ 5x + 6
3) y = x² - 6x - 40
4) y = x²- 8x + 12

Answer 1

To find x-intercepts, factor the quadratic equation and solve for when y = 0. The x-intercepts and the vertex are used to sketch the parabola. Each parabola's sketch will show the x-intercepts and the direction of opening.

Step-by-step explanation:

To find the x-intercepts of a quadratic equation, we can use the quadratic formula, factoring, or completing the square. In this case, we will use factoring. We want to find the values of x when y is equal to 0. So, for each equation, we set y equal to 0 and solve for x:

1. y = x² - 2x - 15: (x - 5)(x + 3) = 0 ➔ x - 5 = 0 or x + 3 = 0 ➔ x = 5 or x = -3
2. y = x² + 5x + 6: (x + 2)(x + 3) = 0 ➔ x + 2 = 0 or x + 3 = 0 ➔ x = -2 or x = -3
3. y = x² - 6x - 40: (x - 10)(x + 4) = 0 ➔ x - 10 = 0 or x + 4 = 0 ➔ x = 10 or x = -4
4. y = x² - 8x + 12: (x - 2)(x - 6) = 0 ➔ x - 2 = 0 or x - 6 = 0 ➔ x = 2 or x = 6

Once we have the x-intercepts, we can sketch the parabola by plotting these points on a graph and drawing a smooth curve that passes through them.