Question

Find the x-intercept of the parabola with vertex (-1,2) and y-intercept (0,-3)

Answer 1

To find the x-intercept of the parabola with the given vertex and y-intercept, we can use the quadratic formula. Substituting the values into the formula, we find x = -1 + sqrt(2) and x = -1 - sqrt(2) as the x-intercepts.

Step-by-step explanation:

To find the x-intercept of a parabola given its vertex and y-intercept, we can use the standard form of a quadratic equation, which is y = ax^2 + bx + c. Since the vertex of the parabola is (-1,2), we can substitute these values into the equation and solve for a, b, and c. We also know that the y-intercept is (0,-3), so we can substitute these values into the equation as well.

After substituting the values and rearranging the equation, we get x^2 + 2x - 1 = 0. To find the x-intercept, we need to solve this quadratic equation. We can use factoring, completing the square, or the quadratic formula to solve it. Let's use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Substituting the values a = 1, b = 2, and c = -1 into the quadratic formula, we get:

x = (-2 ± sqrt(2^2 - 4(1)(-1))) / (2(1))

Simplifying further, we have:

x = (-2 ± sqrt(4 + 4)) / 2

x = (-2 ± sqrt(8)) / 2

x = (-2 ± 2sqrt(2)) / 2

x = -1 ± sqrt(2)

Therefore, the x-intercepts of the parabola are x = -1 + sqrt(2) and x = -1 - sqrt(2).

Answer 2

A graphing calculator shows the vertical scale factor is -5, so the equation is ...
y = -5(x +1)² + 2

Then the x-intercepts are
0 = -5(x +1)² + 2
(x +1)² = 2/5
x +1 = ±√(2/5)

x = -1 ±√(2/5) ≈ {-1.63245553203, -0.36754446797}