What is the axis of symmetry for the equation
Y= x^2-3x+8

Step-by-step explanation:

So to find the axis of symmetry, there are two ways, and I will walk you through both.

1. Axis of Symmetry formula

So first, break down the equation and list down a, b, and c, which in this case is 1, -3, and 8. Then, use the Axis of Symmetry formula, which is x=-b/2a.

x=-b/2a

x=-(-3)/2(1)

x=3/2

So, the axis of symmetry is x=3/2.

2. Vertex form

This method requires knowledge of factoring, and understanding completing the square. So, subtract 8 on both sides to get y-8=x^2-3x.

y-8=x^2-3x

Factor out one.

y-8=1(x^2-3x)

Create a Perfect square trinomial

y-8+1(?)=1(x^2-3x+2.25)

Multiply 1 by 2.25 to complete the square

y-8+2.25=(x-1.5)^2

y-5.75=(x-1.5)^2

y=(x-1.5)^2+5.75

Substitute 1.5, because that will find the x value for the vertex, which is the axis of symmetry.

So, the axis of symmetry is 1.5, or 3/2.

Hope that helps!

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2