SOLUTION: i need to find the x-intercept, y-intercept, axis of symmetry, and vertex of these two problems and don't know how to find any of those 1. f(x)=x^2-6x+8 2. f(x)=-x^2+10x-16

Algebra ->  Functions -> SOLUTION: i need to find the x-intercept, y-intercept, axis of symmetry, and vertex of these two problems and don't know how to find any of those 1. f(x)=x^2-6x+8 2. f(x)=-x^2+10x-16       Log On


   

Question 145531: i need to find the x-intercept, y-intercept, axis of symmetry, and vertex of these two problems and don't know how to find any of those
1. f(x)=x^2-6x+8
2. f(x)=-x^2+10x-16
Please help me!
Found 2 solutions by ankor@dixie-net.com, solver91311:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
find the x-intercept, y-intercept, axis of symmetry, and vertex of these two problems:
;
1. f(x) = x^2 - 6x + 8
y = f(x) so write it:
y = x^2 - 6x + 8
:
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
:
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
:
Axis of symmetry can be found using the formula: x = -b%2F%282a%29
In this equation a=1; b=-6
x = %28-%28-6%29%29%2F%282%2A1%29
x = 6%2F2
x = 3, is the axis of symmetry
:
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
:
graphically you can see all this;
+graph%28+300%2C+200%2C+-2%2C+8%2C+-4%2C+10%2C+x%5E2-6x%2B8%29+
:
This should help you understand what's going on here. Let me know if you need 2nd one explained in the same way.
:
:
2. f(x)=-x^2+10x-16

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You have equations for parabolas.

The vertex of the general parabola f%28x%29=ax%5E2%2Bbx%2Bc is at the point (x,y) where x=-%28b%2F2a%29 and y=f%28-%28b%2F2a%29%29. You just need to calculate -%28b%2F2a%29 and then evaluate the function at that value.

The axis of symmetry is the vertical line that passes through the vertex, and the equation is x=-%28b%2F2a%29. You can get this from the first step above.

The y-intercept is where the graph crosses the y-axis, that is to say, where x=0. Therefore the y-intercept is the point (0,f%280%29). You just need to evaluate f%280%29.

The x-intercepts are at the values of x where the function equals 0. So set your function equal to zero and solve the resulting quadratic equation by whatever means necessary (actually, they factor, and both of your equations will have integer roots). The two solutions you get will be the x-coordinates of the x-intercepts, and the y-coordinates will be 0.