The equation of the parabola is y = -2*(x - 3)² + 8
Let's find the equation:
Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:
y = a*(x - h)² + k
We know that here the vertex is (3, 8), then we will get the equation:
y = a*(x - 3)² + 8
And we know that it passes through (0, -10), then we can replace these values to get:
-10 = a*(0 - 3)² + 8
-10 = 9a + 8
-10 - 8 = 9a
-18/9 = a
-2 = a
The equation is:
y = -2*(x - 3)² + 8
Complete equation:
"Find the parabola with vertex at (3, 8) and passing through the point (0,-10)."