Identify the vertex of the parabola:
y=-x^{2}+5 x+6

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The vertex of the parabola is $(2.5, 12.25)$ .

Steps

Step 1 ：The given equation of the parabola is $y = - x^{2} + 5 x + 6$ .

Step 2 ：The vertex of a parabola given by the equation $y = a x^{2} + b x + c$ is given by the point $(- b / 2 a, f (- b / 2 a))$ .

Step 3 ：In this case, $a = - 1$ , $b = 5$ , and $c = 6$ .

Step 4 ：So, the x-coordinate of the vertex is $- b / 2 a = - 5 / - 2 = 2.5$ .

Step 5 ：To find the y-coordinate of the vertex, we substitute $x = 2.5$ into the equation of the parabola.

Step 6 ：Substituting $x = 2.5$ into the equation gives $y = - {2.5}^{2} + 5 * 2.5 + 6 = 12.25$ .

Step 7 ：Final Answer: The vertex of the parabola is $(2.5, 12.25)$ .