Question

Write a quadratic equation given a vertex of (-5,10), passes through the point (-8,-8), and opens downwards.

a) y = -2(x + 5)^2 + 10
b) y = 2(x + 5)^2 + 10
c) y = -2(x - 5)^2 - 10
d) y = 2(x - 5)^2 - 10

Answer 1

The correct quadratic equation with the vertex (-5, 10), passing through the point (-8, -8), and opening downwards is y = -2(x + 5)^2 + 10. Option a is correct.

Step-by-step explanation:

The question is asking to write a quadratic equation with a given vertex (-5,10), that passes through the point (-8,-8), and which opens downwards.

To find the correct equation, we need to use the vertex form of a quadratic function, which is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola.

Since the vertex is (-5,10), we substitute h with -5 and k with 10 in the vertex form, which gives us y = a(x + 5)^2 + 10.

Next, we need to determine the value of 'a' using the point (-8,-8) that the parabola passes through by plugging x with -8 and y with -8 into the equation to solve for 'a'. This would give us the equation of the parabola that opens downwards if 'a' is negative.

The parabola opens downwards which means 'a' must be negative. By substituting the coordinates of the given point into the equation, we get -8 = a(-8 + 5)^2 + 10. Solving for 'a', we have -8 = a(3)^2 + 10 -> -18 = 9a -> a = -2. Therefore, the correct quadratic equation is option a y = -2(x + 5)^2 + 10.