SOLUTION: Thank you Stan for answering this the first time, however, I did fail to put in that we have to find the x and y intercepts. f(x)=x^2-9x+5 I used the -b/2a and 4ac-b^2/4a formula

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Question 176602: Thank you Stan for answering this the first time, however, I did fail to put in that we have to find the x and y intercepts.
f(x)=x^2-9x+5
I used the -b/2a and 4ac-b^2/4a formulas which makes the problems 9/2(1)and 4(1)(5)-(-9)^2/4(1).
I came up with x=4.5 and y=25.25 Is this right? Thank you so much.
Found 2 solutions by MathLover1, Mathtut:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the x+intercept- where f%28x%29=0
0=x%5E2-9x%2B5
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-9%2Ax%2B5=0 ( notice a=1, b=-9, and c=5)





x+=+%28--9+%2B-+sqrt%28+%28-9%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29 Plug in a=1, b=-9, and c=5




x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29 Negate -9 to get 9




x+=+%289+%2B-+sqrt%28+81-4%2A1%2A5+%29%29%2F%282%2A1%29 Square -9 to get 81 (note: remember when you square -9, you must square the negative as well. This is because %28-9%29%5E2=-9%2A-9=81.)




x+=+%289+%2B-+sqrt%28+81%2B-20+%29%29%2F%282%2A1%29 Multiply -4%2A5%2A1 to get -20




x+=+%289+%2B-+sqrt%28+61+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%289+%2B-+sqrt%2861%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%289+%2B-+sqrt%2861%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%289+%2B+sqrt%2861%29%29%2F2 or x+=+%289+-+sqrt%2861%29%29%2F2



Now break up the fraction



x=%2B9%2F2%2Bsqrt%2861%29%2F2 or x=%2B9%2F2-sqrt%2861%29%2F2



Simplify



x=9%2F2%2Bsqrt%2861%29%2F2 or x=9%2F2-sqrt%2861%29%2F2



So the solutions are:

x=9%2F2%2Bsqrt%2861%29%2F2 or x=9%2F2-sqrt%2861%29%2F2




the y intercept- where x=0
f%280%29=0%5E2-9%2A0%2B5
f%280%29=+5

Solved by pluggable solver: PLOT a graph of a function
Plotting a graph:
graph%28+600%2C+400%2C+-15%2C+15%2C+-15%2C+15%2C+x%5E2-9x%2B5+%29
This solver uses formula rendering system and here's the actual formula that was plotted:

graph( 600, 400, -15, 15, -15, 15, x^2-9x+5 )

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
Find the x-intercepts:
Notice that the x-intercepts of any graph are points on the x-axis and therefore have y-coordinate 0. We can find these points by plugging 0 in for y and solving the resulting quadratic equation (0 = ax2 + bx + c). If the equation factors we can find the points easily, but we may have to use the quadratic formula in some cases. If the solutions are imaginary, that means that the parabola has no x-intercepts (is strictly above or below the x-axis and never crosses it). If the solutions are real, but irrational (radicals) then we need to approximate their values and plot them.
Find the y-intercept:
The y-intercept of any graph is a point on the y-axis and therefore has x-coordinate 0. We can use this fact to find the y-intercepts by simply plugging 0 for x in the original equation and simplifying. So the y-intercept of any parabola is always at (0,c).
f(x)=x^2-9x+5
:
setting x to zero
:
y=0%5E2-9%280%29%2B5=5
:
so y=c or y=5
:
x=8.49 and x=.59
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-9x%2B5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-9%29%5E2-4%2A1%2A5=61.

Discriminant d=61 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+61+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+61+%29%29%2F2%5C1+=+8.40512483795333
x%5B2%5D+=+%28-%28-9%29-sqrt%28+61+%29%29%2F2%5C1+=+0.594875162046673

Quadratic expression 1x%5E2%2B-9x%2B5 can be factored:
1x%5E2%2B-9x%2B5+=+%28x-8.40512483795333%29%2A%28x-0.594875162046673%29
Again, the answer is: 8.40512483795333, 0.594875162046673. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-9%2Ax%2B5+%29