Question

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

Answer 1

The vertex of the parabola with the equation
`y = -2x^2 + 8x - 5` is found by using the formula x = -b/(2a). The vertex coordinates are (2, -5).

Step-by-step explanation:

To find the vertex of the parabola with the equation
`y = -2x^2 + 8x - 5,` we need to use the vertex form of a quadratic equation, which is
`y = a(x-h)^2 + k`, where (h, k) is the vertex of the parabola. For the given equation, a = -2. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation y = ax2 + bx + c.

Here's a step-by-step method to find the vertex:

Identify the coefficients: a = -2, b = 8.

Use the formula x = -b/(2a) to find the x-coordinate of the vertex: x = -8/(2*(-2)) = 2.

Plug this x-value into the original equation to find the y-coordinate: y = -2(2)2 + 8*2 - 5 = -16 + 16 - 5 = -5.

Therefore, the vertex of the parabola is (2, -5).

Answer 2

hello :
y = -2x² + 8x - 5 = -2(x²-4x-5)
but : x²-4x = (x²-4x +2²)-2²
= (x-2)² -4
y = -2 ((x-2)²-9)
y = -2 (x-2)²+18
the vertex is A(2,18)