SOLUTION: a) Without solving the equation (or factoring), determine the solutions to the equation x2 – 6x = 0 using only the graph. Answer: Explain how you obtain your answer(s) by looking

Algebra ->  Graphs -> SOLUTION: a) Without solving the equation (or factoring), determine the solutions to the equation x2 – 6x = 0 using only the graph. Answer: Explain how you obtain your answer(s) by looking       Log On


   

Question 632260: a) Without solving the equation (or factoring), determine the solutions to the
equation x2 – 6x = 0 using only the graph. Answer: Explain how you obtain your answer(s) by looking at the graph in a brief sentence:
b) Does this function have a maximum or a minimum? Answer: Explain how you obtain your answer by looking at the graph in a brief sentence:
c) What are the coordinates of the vertex in (x, y) form? Answer:
d) What is the equation of the axis of symmetry for this parabola?
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B0+=+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=%28-6%29%5E2-4%2A1%2A0=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+36+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%28-6%29-sqrt%28+36+%29%29%2F2%5C1+=+0

Quadratic expression 1x%5E2%2B-6x%2B0 can be factored:
1x%5E2%2B-6x%2B0+=+1%28x-6%29%2A%28x-0%29
Again, the answer is: 6, 0. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B0+%29

b. The function has a minimum value because it opens upward and has a lowest point.
c. The vertex (lowest point) is (3,-9).
c. The axis of symmetry is x = 3.