Determine the points of intersection of the line y = -2x + 7 and the parabola y = 2x2 + 3x - 5.

(-4, 15), (1.5, 4)

This is easily solved using a graphing calculator. (See attached.)

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Algebraically, the solution is found by equating the expressions for y:

... -2x +7 = y = 2x² +3x -5

... 2x² +5x -12 = 0 . . . . rearranged to standard form

... (2x -3)(x +4) = 0 . . . . factor

The x-values of the points of intersection are those that make these factors be zero:

... 2x-3 = 0 ⇒ x = 3/2

... x+4 = 0 ⇒ x = -4

The linear equation is the easiest to use to find the corresponding y-values.

... for x = 3/2, y = -2(3/2) +7 = 4

... for x = -4, y = -2(-4) +7 = 15

The points of intersection are (-4, 15) and (3/2, 4).

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

slope =   (y2 -y1) ÷ (x2 -x1)

slope = (0 -0) / (-5, -7)

slope = 0 / -12 = 0

the slope of the line is zero.   it is perfectly horizontal.

step-by-step explanation: