Find the vertex of the parabola whose equation is y = -2x² + 8x - 5.

Solution:

We have to find the vertex of the parabola.

For any parabola equation of the type y = ax² + bx + c, the vertex is given by (h, k)

Where, h = -b/2a and k = (4ac - b²)/4a.

Given, the equation is y = -2x² + 8x - 5

Here, a = -2, b = 8 and c = -5

So, h = -8/2(-2)

h = -8/-4

h = 2

4ac = 4(-2)(-5)

4ac = 40

So, k = [40 - (8)²]/4(-2)

k = (40 - 64)/-8

k = -24/-8

k = 3

Therefore, the vertex is (2, 3).

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Find the vertex of the parabola whose equation is y = -2x² + 8x - 5.

Summary:

The vertex of the parabola whose equation is y = -2x² + 8x - 5 is (2, 3).