Question

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

Answer 1

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

Answer 2

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