SOLUTION: the problem is 3x^+x-5 I need to find the x intercept and the vertex . I am not sure how to set up the equation or what numbers go where. HELP PLEASE

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Question 162673: the problem is 3x^+x-5 I need to find the x intercept and the vertex . I am not sure how to set up the equation or what numbers go where. HELP PLEASE
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
See this for a fairly detailed look at this issue --> http://www.analyzemath.com/quadratics/vertex_problems.html
I assume you meant 3x%5E2%2Bx-5
Any point that is an x axis intercept must have a y coordinate value of 0. So to solve for those points. solve
3x%5E2%2Bx-5=0 You can use quadratic equation for that.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B1x%2B-5+=+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=%281%29%5E2-4%2A3%2A-5=61.

Discriminant d=61 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+61+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+61+%29%29%2F2%5C3+=+1.13504161265111
x%5B2%5D+=+%28-%281%29-sqrt%28+61+%29%29%2F2%5C3+=+-1.46837494598444

Quadratic expression 3x%5E2%2B1x%2B-5 can be factored:
3x%5E2%2B1x%2B-5+=+3%28x-1.13504161265111%29%2A%28x--1.46837494598444%29
Again, the answer is: 1.13504161265111, -1.46837494598444. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B1%2Ax%2B-5+%29


The URl above gives you a formula for finding the vertex. Here are two others ways
1)if you know deriviatives, take the first derivative and set that to 0. Then solve for x. Use that x vlaue to find the corresponding y in the original equation.
2) find the x value that is the average of the 2 x intercepts. That point is on the line that 'splits' the parabola (the line about which the parabola has symmetry). Find that x value and plug it into the original equation to find the y value.