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

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) (Show Source): You can put this solution on YOUR website!
a. First complete the square

Add 5(-2/2)^2 to both sides to complete the square
Factor the right side
There's the completed square.
In the basic equation
} h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. So in
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 and have the same graphs (because they are equivalent)

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