Question 2 (20 points)Write an equation for the parabola whose vertex is at (-8, 4) and passes through (-6, -2).

The equation of the parabola is y = -1.5(x + 8)² + 4 in the vertex formStep-by-step explanation:The equation of the parabola in the vertex form is y = a(x - h)² + kwhere1. (h , k) are the coordinates of its vertex point2. x and y are the coordinates of a general point on the parabola∵ The equation of the parabola is y = a(x - h)² + k∵ The vertex of the parabola is (-8 , 4)∴ h = -8 and k = 4∵ The parabola passes through point (-6 , -2)∴ x = -6 and y = -2- Substitute these values in the equation above to find value of a∴ -2 = a(-6 - -8)² + 4∴ -2 = a(-6 + 8)² + 4∴ -2 = a(2)² + 4∴ -2 = 4a + 4- Subtract 4 from both sides∴ -6 = 4a- Divide both sides by 4∴ a = -1.5∴ The equation of the parabola in the vertex form is:    y = -1.5(x + 8)² + 4The equation of the parabola is y = -1.5(x + 8)² + 4 in the vertex formLearn more:You can learn more about the parabola in brainly.com/question/9390381#LearnwithBrainly