Question

Find the vertex of the following function. The vertex of the equation (Ax² + Bx + C) is calculated by the formula (Vₓ = -fracB/2A) and (V_y = fleft(-fracB/2A)).

- a) (Vₓ = -1, V_y = 3)
- b) (Vₓ = 2, V_y = 6)
- c) (Vₓ = -1, V_y = 1)
- d) (Vₓ = 1, V_y = -1)

Answer 1

The vertex of the quadratic function x² + 10x - 200 is (Vₓ = -5, V_y = -225).

Step-by-step explanation:

To find the vertex of a quadratic function in the form Ax² + Bx + C, you can use the formula Vₓ = -B/2A and V_y = f(-B/2A). In this case, the equation is x² + 10x - 200, so A = 1, B = 10, and C = -200. Plugging these values into the formula, we get Vₓ = -10/2(1) = -5 and V_y = f(-10/2(1)) = f(-5) = (-5)² + 10(-5) - 200 = 25 - 50 - 200 = -225. Therefore, the vertex is (Vₓ = -5, V_y = -225).