Question

What is the vertex of the quadratic function f(x) = -2x² + 5x - 3?

a) Vertex is (3, 12)
b) Vertex is (-1/2, -15)
c) Vertex is (-5/4, -21/16)
d) Vertex is (0, -3)

Answer 1

The vertex of the quadratic function f(x) = -2x² + 5x - 3 is found using the formula for the vertex -b/2a. After calculation, the vertex is (5/4, -21/16), which matches option c).

Step-by-step explanation:

To find the vertex of the quadratic function f(x) = -2x² + 5x - 3, we need to use the formula for the x-coordinate of the vertex, which is -b/2a for a quadratic function in standard form ax² + bx + c. In this case, a = -2 and b = 5. Thus, the x-coordinate of the vertex is -5 / (2 * -2) = 5/4. To find the y-coordinate, we substitute x = 5/4 back into the original function:

f(5/4) = -2(5/4)² + 5(5/4) - 3 = -2(25/16) + (25/4) - 3 = -50/16 + 100/16 - 48/16 = 2/16 = -21/16.

Therefore, the vertex of the given function is (5/4, -21/16), which corresponds to option c).