Rewrite the equation f (x) =2x^2 +12x+7 to the form f (x) =a (x-h)^2+k

Mathematics

2 answers:

Alborosie3 years ago

5 0

Complete theh square

isolate x terms
factor out coefient of x^2 term
take 1/2 of 1st degree coefient and square it, add positive and negative inside parnthasees, expand

f(x)=(2x^2+12x)+7
f(x)=2(x^2+6x)+7
6/2=3, 3^2=9
f(x)=2(x^2+6x+9-9)+7
f(x)=2((x+3)^2-9)+7
f(x)=2(x+3)^2-19+7
f(x)=2(x+3)^2-12

Volgvan3 years ago

4 0

You do have to complete the square on part of the problem. Follow my steps in the picture. If you graph the original problem and the answer you should get the same graph. I checked my answer.

You might be interested in

1. Find the phase shift of the function y = 5cos(2x + pi/2).

kolezko [41]

Answer:

see explanation

Step-by-step explanation:

The cosine function in standard form is

y = acos(bx + c)

where a is the amplitude, period = $\frac{2\pi }{b}$ and

phase shift = - $\frac{c}{b}$

here b = 2 and c = $\frac{\pi }{2}$ , thus

phase shift = - $\frac{\frac{\pi }{2} }{2}$ = - $\frac{\pi }{4}$

the amplitude = | a |

which has a maximum of a and a minimum of - a

y = 4cosx ← has a maximum value of 4

5 0

3 years ago

Use matrix addition to solve this equation

REY [17]

Answer:

c11 = 8
c31 = 20
c22 = 14

Step-by-step explanation:

The sum of two matrices is the sum of corresponding terms.

$\left[\begin{array}{ccc}3&1&0\\-1&2&4\\9&7&-2\end{array}\right] +\left[\begin{array}{ccc}5&2&4\\1&12&3\\11&3&-2\end{array}\right] =\left[\begin{array}{ccc}8&3&4\\0&14&7\\20&10&-4\end{array}\right]$