SOLUTION: Hi Can I have some help concerning this problem? Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts. y = 6x^2 + 7x + 1 (v

Algebra ->  Equations -> SOLUTION: Hi Can I have some help concerning this problem? Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts. y = 6x^2 + 7x + 1 (v      Log On


   

Question 127701: Hi Can I have some help concerning this problem?
Sketch the graph of the given parabola and state the coordinates of its vertex and its intercepts.
y = 6x^2 + 7x + 1
(vertex)
y = (y-intercept)
x = (leftmost x-intercept)
x = (rightmost x-intercept)
Answer by JessicaGill(40) About Me  (Show Source):
You can put this solution on YOUR website!
Using the quadratic solver here are the steps
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B7x%2B1+=+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=%287%29%5E2-4%2A6%2A1=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+25+%29%29%2F2%5C6+=+-0.166666666666667
x%5B2%5D+=+%28-%287%29-sqrt%28+25+%29%29%2F2%5C6+=+-1

Quadratic expression 6x%5E2%2B7x%2B1 can be factored:
6x%5E2%2B7x%2B1+=+6%28x--0.166666666666667%29%2A%28x--1%29
Again, the answer is: -0.166666666666667, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B7%2Ax%2B1+%29


You can also use the vertex formula x=-%28b%2F2a%29 to find the x coordinate of the vertex and the axis of symmetry. Once you find the x value, substitute the value for x in the original equation and find the y coordinate of the vertex.
Then choose two x values either two the left or the right of the vertex and sustitute and solve for the y coordinates to the x values.
Then graph the reflection of each of those points and graph the parabola points and sketch the graph. You will have to estimate the points from the graph above.