Determine the points of intersection of the line y = -2x + 7 and the parabola y = 2x2 + 3x - 5.
1 answer:
Answer:
Step-by-step explanation:
The x-values of those points can be found by equating the expressions for y, then solving for x.
... -2x +7 = 2x² +3x -5
... 2x² +5x -12 = 0 . . . . . . . . subtract the left side to put into standard form
This can be factored by looking fro two factors of 2·(-12) = -24 that add to give 5, the x-coefficient. Those factors are 8, -3.
... 2x² +8x -3x -12 = 0 . . . . rewrite the middle term
... 2x(x +4) -3(x +4) = 0 . . . factor by pairs
... (x +4)(2x -3) = 0 . . . . . . . complete factorization
... x = -4, x = 3/2 . . . . . . . . values of x that make the factors be zero
The corresponding y-values are ...
... for x = -4, y = -2(-4) +7 = 15
... for x = 3/2, y = -2(3/2) +7 = 4
The points of intersection are (-4, 15) and (3/2, 4).
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Answer: c.(3, 25) and (7, 9)
y = –x^2 + 6x + 16 and y = –4x + 37
Plug in -4x+37 for y in first equation . It becomes
Combine like terms. add 4x and subtract 37 on both sides
Divide the whole equation by -1 to remove negative sign from -x^2
Now factor the left hand side
(x-7)(x-3) = 0
x-7 =0 and x-3=0
x= 7 and x=3
Now we find out y using y = –4x + 37
when x= 7 , then y=-4(7) +37 = 9
when x= 3, then y=-4(3) + 37 = 25
We write solution set as (x,y)
(7,9) and (3,25) is our solution set