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

User Verdagon
by
6.4k points

1 Answer

1 vote

Answer:

x = 2

Explanation:

A graph shows the axis of symmetry easily. It is the x-coordinate of the vertex.

x = 2

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You can rearrange the equation to ...

y -7 = 4x -x^2

y -7 = x(4 -x)

The axis of symmetry is halfway between x-values that give the same y-value. Here, y=7 for x=0 and for x=4. That is, the right side of this equation is zero at those x-values. The axis of symmetry is halfway between, at x = (0+4)/2 = 2

The axis of symmetry is x=2.

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Alternate solutions

In standard form,

ax^2 +bx +c = y

the axis of symmetry is ...

x = -b/(2a)

Putting this equation into that form, we have ...

-x^2 +4x +7 = y

x = -(4)/(2(-1))

x = 2 . . . . axis of symmetry

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We can rearrange the equation to vertex form.

y -7 = -x^2 +4x

y -7 -4 = -(x^2 -4x +4) . . . . . add the square of half the x-coefficient inside parentheses. Add an equal amount to the other side of the equation.

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

This tells us the vertex of the graph is (2, 11), so the axis of symmetry is x=2.

What is the axis of symmetry for the graph of y – 4x = 7 – x2 ?-example-1
User HibernatedGuy
by
6.0k points
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