Answer to Question #91576 in Geometry for Sajid

Question

Q. Choose the correct answer.
Q. The vertex of parabola y=(-1)/2x2-x+4 is
a. (1,9/4)
b.( -1,9/4)
c. (9/2, -1)
d. (9/2, 9/2)

Answer 1

The vertex of parabola $y=-\frac{1}{2}{x^2}-x+4$ is at $(-1,\frac{9}{2})$. Thus, there is no correct answer in the list of variants a, b, c, d.

Explanation:

Here, a =$-\frac{1}{2}$  and b = -1

So, the x -coordinate of the vertex is:

$x = -\frac{b}{2а} = -\frac{-1}{2*(-\frac{1}{2})}=-\frac{-1}{-1}=-1$.

Substituting in the original equation to get the

y -coordinate, we get:

$y=-\frac{1}{2}{x^2}-x+4 = -\frac{1}{2}{(-1)^2}-(-1)+4 = -\frac{1}{2} + 1 +4 = 4.5 = -\frac{9}{2}$

Answer. The vertex of parabola $y=-\frac{1}{2}{x^2}-x+4$ is at $(-1,\frac{9}{2})$. Thus, there is no correct answer in the list of variants a, b, c, d.