**Problem: Writing the Equation of a Parabola** Write an equation for a parabola with x-intercepts at (-3, 0) and (5, 0) which passes through the point (4, -28). **Instructions:** 1. Use the intercept form of a quadratic equation: \( y = a(x - p)(x - q) \). 2. Identify the x-intercepts as \( p = -3 \) and \( q = 5 \). 3. Substitute the point (4, -28) into the equation to solve for \( a \). **Steps:** 1. Begin with the general equation: \( y = a(x + 3)(x - 5) \). 2. Substitute the point (4, -28) into the equation: \[ -28 = a(4 + 3)(4 - 5) \] 3. Simplify and solve for \( a \): \[ -28 = a(7)(-1) \] \[ -28 = -7a \] \[ a = 4 \] **Final Equation:** The equation of the parabola is: \[ y = 4(x + 3)(x - 5) \]

Q: Graph the equation (x+2)^2 +(y+3)^2 = 4 below. Label all intercepts. Is ((-2,-3) a point on the…

A:

Q: A parabola is given by the equation y = x^2 - 4x + 6. Find k so the line of equation y = 2x - k does…

A: We have to find the value of k for which the line intersect the parabola at two distinct points. To…

Q: Give 3 points that lie on the parabola y=x^2-5x-2

A:

Q: Determine the vertex of a parabola y=-2x^2+15x using calculus (use first principles to solve)

A:

Q: Determine the equation of the quadratic function that passes through (-3, 20) if its x-intercepts a…

A:

Q: Determine an equation to represent the following parabola in intercept form

A: This question is about finding equation of curve by its points

Q: Determine an equation for the parabola whose vertex is (- 2, 3) and goes through the point (4, - 6)

A: Given (h, k)=(-2, 3) and parabola passes through (4, -6).

Q: What is an equation of the line that passes through the points (3,-8) and (1, -2)? Put your answer…

A: