SOLUTION: Hi, I'm having trouble with the following function. Can I please have some help solving? A quadratic function is given. f(x) = 10x^2 +x

SOLUTION: Hi, I'm having trouble with the following function. Can I please have some help solving? A quadratic function is given. f(x) = 10x^2 +x - 1 (a) Express the quadratic function

Question 127805: Hi, I'm having trouble with the following function. Can I please have some help solving?
A quadratic function is given.
f(x) = 10x^2 +x - 1
(a) Express the quadratic function in standard form.
f(x) = a(x - h)^2 + k where
a =
h =
k =
(c) Find its minimum or maximum value.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

Start with the given equation

Add to both sides

Factor out the leading coefficient

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation

Now factor to get

Distribute

Multiply

Now add to both sides to isolate y

Combine like terms

Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor. Also "a" tells us which direction the parabola opens.

So in this case the vertex is (,) and the parabola opens upward since

Check:

Notice if we graph the original equation we get:

Graph of . Notice how the vertex is (,).

Notice if we graph the final equation we get:

Graph of . Notice how the vertex is also (,).

So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.

c)

The min or max occurs at the vertex and the max/min value is the y value of the vertex. So in this case the minimum is
RELATED QUESTIONS
Hi Can I have some help with the following function? A function f is given. f(x) =... (answered by jim_thompson5910)

Hi can I have some help concerning functions? A quadratic function is given.... (answered by rothauserc)

Hi can I have some help concerning functions? A quadratic function is given. f(x) =... (answered by scott8148)

Hi Can I have some help concerning functions? A quadratic function is given. f(x) =... (answered by jim_thompson5910)

Hi Can I have some help with the following function? Consider the following. f(x) =... (answered by stanbon)

Hi all, Im having trouble with the following Function and Domain problem. I have already... (answered by stanbon)

Hi, I'm having trouble solving this problem and I can sure use a little help. I would... (answered by stanbon,solver91311)

I am having trouble with Graphing the quadratic function f(x)= x^2 + X - 12 (answered by josgarithmetic)

Hi Can I have some help with this function? Use the function to evaluate the indicated (answered by stanbon)