Question

What is the axis of symmetry for the graph of y – 4x = 7 – x2

Answer 1

y - 4 x = 7 - x²
y = - x ² + 4 x + 7 ( this is a quadratic function )
x = - b / 2 a, where: a = - 1 and b = 4
x = - 4 / ( - 2 ) = 2
Answer:
The axis of symmetry for the graph is x = 2

Answer 2

we know that

The equation in vertex form of a vertical parabola is equal to

`y=a(x-h)^(2)+k`

where

(h,k) is the vertex of the parabola

and the axis of symmetry is equal to the x-coordinate of the vertex

so

`x=h` -----> equation of the axis of symmetry

In this problem we have

`y-4x=7-x^(2)`

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`y-7=-x^(2)+4x`

`y-7=-(x^(2)-4x)`

Complete the square. Remember to balance the equation by adding the same constants to each side

`y-7-4=-(x^(2)-4x+4)`

`y-11=-(x^(2)-4x+4)`

Rewrite as perfect squares

`y-11=-(x-2)^(2)`

`y=-(x-2)^(2)+11`

the vertex is the point
`(2,11)`

therefore

the answer is

The axis of symmetry is

`x=2`

see the attached figure to better understand the problem