can you help me answer those two questions?

Question

1) Contrat linear and quadratic equations.
2) How you would complete the square on
x square- 16x= 4?

Answer 1

2)
x^2 - 16x - 4 = 0
x^2 - 16x + 8^2 - 8^2 - 4 =0
(x - 8)^2 - 64 - 4 = 0
(x - 8)^2 - 68 = 0
( x - 8 - sqrt68)( x - 8 + sqrt68) = 0
( x - 8 - 2sqrt17)(x - 8 + 2sqrt17) = 0

Answer 2

Hi,

First, linear equations have straight lines as their graphs. They do not have exponents in their equations and the variables are not multiplied together. Examples of equations of linear graphs are:

2x + 3y = 12 in standard form
y = 1/2x - 7 in slope-intercept form
y - 5 = -3/4(x + 12) in point slope form.
x = 4
y = -3

Quadratic equations are equations that can be written in the form ax^2 + bx + c, where a, b, and c are numbers. Notice it has an exponent in its squared x term. This type of quadratic has a parabola as its graph. Its graph is kind of a U shaped graph that continues to get wider as it opens. Examples of quadratics like this include:

y = 2x^2 + 5x + 5
y = x^2 - 4
x = 3y^2 - 12y + 12
y = 4(x - 5)^2 + 3

2) To complete the square on x^2 - 16 x = 4, the constant has already been moved to the right side and there is no number in front of x^2 that you'd have to divide by first. So, to complete the square, you always multiply one half times the x term's coefficient, square that number and add it to both sides.

1/2 x -16 = -8 ( half of -16)

(-8)^2 = 64 ( negative 8 squared)

x^2 - 16x + 64 = 4 + 64 (add 64 to both sides)

The left hand side can now be factored into a binomial squared. It will always start with x and end with the number you got when you took half of your coefficient.

You can also combine like terms on the right.

(x - 8)^2 = 68

Now square root both sides, putting a +/- in front of the radical on the right.

sqrt[ (x - 8)^2 ] = +/- sqrt(68)

The radical and the exponent cancel each other out on the left. You need to factor the number on the right and simplify the radical as far as possible without getting decimals.

Realize that 68 = 2 x 2 x 17, so with a pair of 2s, you can take out a 2 from the radical.

x - 8 = +/- 2 sqrt( 17)

Now get the x alone by adding 8 to both sides. Write that 8 in front of the +/- sign on the right side.

x = 8 +/- 2 sqrt(17)

Your 2 answers are 8 + 2sqrt(17) and 8 - 2sqrt(17).

I hope that helps!! :-)

Answer 3

1. for linear equation, the general formula is y=mx+c. so all u got to do is to find the gradient,m with y1-y2/x1-x2 and substitute the y and x with the coordinates given. from there, c can be found. whereas for the quadratic equation, use the general formula, y=ax^2+bx+c.... from there substitute the coordinates and use simaltaneous equation to solve out a,b and c.

2. x=1/2
thats bcos... the only way for 16 to turn into 4 is by division. and since 4^2 gives u 16, 16^1/2 will gives u 4. its like normal equation like 2x=4 which gives x=4/2... x=2. with 4x=2... to find x... x=2/4...x=1/2

Answer 4

2 Problem

Completing the square

x² - 16x = 4

x² - 16x + ______= 4 +______

x² - 16x + 64 = 4 + 64

(x - 8)(x - 8) = 68

(x - 8)² = 68

(√x - 8)² = ± √68

x - 8 = ± √68

x - 8 + 8 = 8 ± √68

x = 8 ± 8.246211251

- - - - - -

Solving for +

x = 8 + 8.24621151

x = 16.24621125

- - - - - - -

Solving for -

x = 8 - 8.246211251

x = 0.24621151

- - - - - - -s-

Answer 5

x^2 -16x +64( 1/2 the no in front of x and sq it)
or
x^2-16x+64=4+64(add to both sides)