Question 145531
find the x-intercept, y-intercept, axis of symmetry, and vertex of these two problems:
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1. f(x) = x^2 - 6x + 8
y = f(x) so write it:
y = x^2 - 6x + 8
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The x intercept occurs when y=0, make the equation = 0 and solve for x
x^2 - 6x + 8 = 0
Factor
(x-4)(x-2) = 0
x = +4 and x = + 2, these are the x intercepts
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y intercept occurs when x=0, substitute 0 for x in the equation, and find y
y = 0^2 - 6(0) + 8
y = 8; you can see in any equation the y intercept is the numerical value
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Axis of symmetry can be found using the formula: x = {{{-b/(2a)}}}
In this equation a=1; b=-6
x = {{{(-(-6))/(2*1)}}}
x = {{{6/2}}}
x = 3, is the axis of symmetry
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Vertex is the x/y values for the max or min and occurs at the axis of symmetry
Substitute 4 for x and find the y value:
y = 3^2 - 6(3) + 8
y = 9 - 18 + 8
y = -1; the vertex occurs at: x=3, y =-1
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graphically you can see all this;
{{{ graph( 300, 200, -2, 8, -4, 10, x^2-6x+8) }}}
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This should help you understand what's going on here. Let me know if you need 2nd one explained in the same way.
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2. f(x)=-x^2+10x-16