SOLUTION: Hi Can I have some help concerning functions? A quadratic function is given. f(x) = 6x^2 + x + 1 (a) Express the quadratic function in standard form. f(x) = a(x

SOLUTION: Hi Can I have some help concerning functions? A quadratic function is given. f(x) = 6x^2 + x + 1 (a) Express the quadratic function in standard form. f(x) = a(x - h)^2 + k

Question 127713: Hi Can I have some help concerning functions?
A quadratic function is given.
f(x) = 6x^2 + x + 1
(a) Express the quadratic function in standard form.
f(x) = a(x - h)^2 + k where
a =
h =
k =
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation

Subtract from 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.

RELATED QUESTIONS
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, I'm having trouble with the following function. Can I please have some help solving? (answered by jim_thompson5910)

Please help explain these: A quadratic function is given (a) Express the quadratic... (answered by josgarithmetic)

Hi Can I have some help with the following function? A function f is given. f(x) =... (answered by jim_thompson5910)

Hello! A quadratic function is given. f(x) = 3 - 36x - 36x^2 (a) Express the... (answered by edjones)

A quadratic function is given (a) Express the quadratic function in standard form (b) (answered by josgarithmetic)

Hi! A quadratic function of f is given. f (x) = 3x^2 + 6x - 7 Find its vertex and (answered by nerdybill,gracia143)

Can someone please help me understand graph's before my final next week. I have 2... (answered by rapaljer,Nate)