SOLUTION: I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-inter

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-inter      Log On


   

Question 214894: I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-intercept,(e) find the zeros, and (f) graph the function
the equation is: -x(x-3)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
For:
-x%28x-3%29 rewrite as y+=+-x%5E2%2B3x
Find:
a) The graph opens downward as indicated by the negative value of the x%5E2 term.
b) The axis of symmetry (AOS) is given by:
x+=+-b%2F2a where: a = -1 and b = 3.
x+=+%28-3%29%2F2%28-1%29
highlight%28x+=+3%2F2%29 This is the equation of the AOS.
c) The vertex is lies on the AOS and is found by using the equation of the AOS for the x-coordinate, then substituting this into the given quadratic equation to solve for the corresponding y-coordinate.
y+=+-x%5E2%2B3x Substitute x+=+3%2F2
y+=+-%283%2F2%29%5E2%2B3%283%2F2%29 Evaluate.
y+=+-%289%2F4%29%2B%289%2F2%29
y+=+9%2F4
The vertex is at: (3/2, 9/4)
d)
The y-intercept is found by setting x = 0 in the given quadratic equation and solving for y.
y+=+-x%5E2%2B3x Substitute x = 0.
y+=+0
The y-intercept is at: (0, 0)
e)
The zeros are found by setting the given quadratic equation equal to zero and solving.
-x%5E2%2B3x+=+0 Factor a -x.
-x%28x-3%29+=+0 Apply the zero product rule:
-x+=+0 or x-3+=+0 so that...
highlight%28x+=+0%29 or highlight%28x+=+3%29
The zeros are at (0, 0) and (3, 0)
f)
Graph: y+=+-x%5E2%2B3x
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C-x%5E2%2B3x%29