SOLUTION: f(x)=5x^2-10x+3 a. find the vertex b. find the axis of symmetry c. determine whether there is a maximum or minimum value and find the value d. find the range e graph the fun

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: f(x)=5x^2-10x+3 a. find the vertex b. find the axis of symmetry c. determine whether there is a maximum or minimum value and find the value d. find the range e graph the fun      Log On


   

Question 71903This question is from textbook algebra and trigonometry
: f(x)=5x^2-10x+3
a. find the vertex
b. find the axis of symmetry
c. determine whether there is a maximum or minimum value and find the value
d. find the range
e graph the function
I would really appreciate some help with this question. I don't understand the explanation the book gives
Thank you This question is from textbook algebra and trigonometry

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a. First complete the square
y=5x%5E2-10x%2B3
y-3=5x%5E2-10x
y-3%2B5=5%28x%5E2-2x%2B1%29Add 5(-2/2)^2 to both sides to complete the square
y%2B2=5%28x-1%29%5E2Factor the right side
y=5%28x-1%29%5E2-2There's the completed square.
In the basic equation
y=a%28x-h%29%5E2%2Bk} h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. So in
y=5%28x-1%29%5E2-2 the vertex is (1,-2) you can verify this by graphing


b. The axis of symmetry is at the vertex, so the axis of symmetry is x=1


c. The min or max of any quadratic is always at the vertex. So in this case the min is at (1,-2) (the min is the lowest point on the curve)


d. The range is all of the outputs of the function (or all the y-values). So the range is all the y's from -2 to infinity or could be written as [-2,infinity)


e. Both y=5%28x-1%29%5E2-2 and y=5x%5E2-10x%2B3 have the same graphs (because they are equivalent)
graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+5x%5E2-10x%2B3%29