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never [62]
3 years ago
13

Describe the graph that would be used to solve the equation-x^2 + 4 = x+2

Mathematics
1 answer:
Rzqust [24]3 years ago
5 0

Answer:

The values of x are x = -2 and x= 1.

Step-by-step explanation:

The given equation -x²+4 = x+2 can be written in the form of two functions as

y = -x²+4 which is a function representing parabola and

y = x+2 which is a straight line.

Now we will solve the given equation to find their points of intersection on graph. Their points of intersections will be the answer.

-x²+4 = x+2

-x²+4-x = x+2-x

-x²-x+4 = 2

-x²-x+4-2 = 2-2

-x²-x+2 = 0

Or x²+x-2=0

Now we will factorize the equation.

x²+2x-x-2=0

x(x+2)-1(x+2) = 0

(x+2)(x-1) = 0

x+2 = 0 ⇒x = -2

x-1 = 0 ⇒x = 1

For x = 1, y will be 3

and for x = -2, y will be 0

Now we can see the graph for the given coordinates (-2,0) and (1,3).



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Write an equation of the line that passes through (−1,3) and is parallel to the line y=2x+2.
MA_775_DIABLO [31]

The equation of the line that passes through (−1,3) and is parallel to the line y = 2x + 2 in slope intercept form is y = 2x + 5

<h3><u>Solution</u>:</h3>

Given that line passes through (-1, 3) and parallel to line y = 2x + 2

We have to find the equation of the line

Let us first find the slope of the line

<em><u>The slope intercept form of line is given as:</u></em>

y = mx + c  ---- eqn 1

where "m" is the slope of the line and "c" is the y-intercept

Comparing the given line equation y = 2x + 2 with y = mx + c,

We get slope "m" = 2

The slope of parallel lines are equal

Hence slope of the line which is parallel to y = 2x + 2 is also 2

Now let us find the equation of line with slope "m" = 2 and passes through point (-1, 3)

Substitute (x, y) = (-1, 3) in eqn 1 to find value of "c"

3 = 2(-1) + c

3 = -2 + c

c = 5

Now substitute "c" = 5 and m = 2 in eqn 1 to get equation of required line

y = 2x + 5

Thus the equation of line in slope intercept form is y = 2x + 5

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