What value of x will result in an expression that is the easiest to solve without the use of a calculator?
1 answer:
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Answer:
x = 2
Step-by-step 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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<em>Alternate solutions</em>
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.
