Mathematics: Y=-x^2+6x-5 1. what is the vertex? 2. does it open up or down? 3. what is the y-intercept?

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Y=-x^2+6x-5 1. what is the vertex? 2. does it

ghwolf4p0m7x0

13.01.2022

1. Vertex: (3,4)

2. It opens down.

3. The y-intercept is -5

Step-by-step explanation:

1. For a quadratic function in the form y=ax^2+bx+c , you can calculate the x-coordinate of the vertex with:

$x=\frac{-b}{2a}$

Then, given the function y=-x^2+6x-5 , you can identify that:

$b=6\\a=-1$

Substituting, you get:

$x=\frac{-6}{2(-1)}=3$

Substitute x=3 into y=-x^2+6x-5 to find the y-coordinate of the vertex:

y=-(3)^2+6(3)-5=4

Then the vertex is at (3,4)

2. You identified above the value of "a". This is:

a=-1

Then, since , the parabola opens down.

3. Substitute x=0 into the function and solve for "y":

$y=-(0)^2+6(0)-5\\y=-5$

Therefore, the y-intercept is -5

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