Find the values of x for which f(x) = g(x). (Enter your answers as a comma-separated list.) f(x) = x2, g(x) = x + 20

Question

Find the values of x for which f(x) = g(x).

 (Enter your answers as a comma-separated list.)

f(x) = x²,    g(x) = x + 20

Answer 1

x^2 is a standard parabola with vertex at the origin

x+20 is a straight line with y-intercept = 20 and x-intercept = -20

The line crosses the parabola potentially two times, one to the right of the y-axis where x>0 and one to the left of the y-axis where x<0, There should be a positive and a negative solution for x

x^2 = x+ 20

plug in some simple integers for x

x=1 gives 1=21

x=2 gives 4 =22

x=3 gives 9 = 23

x=4 gives 16 =24

x=5 gives 25 = 25

5 is one solution

the other solution is negative

x=-1 gives 1 = 19

x=-2 gives 4 = 18

x= -3 gives 9 = 17

x=-4 gives 16 = 16

-4 is the other solution

for each solution there is a factor

x=5 or x-5=0 has (x-5) as a factor

x=-4 or x+4=0 has (x+4) as a factor

multiply the factors together

(x-5)(x+4) = x^2 -x -20 = 0

or x^2 = x+20

f(x) = g(x)

when x = -4 or 5

x= -4, 5

Answer 2

Set the equations equal to each other and solve

x²=x+20 Subtract x and subtract 20 from both sides of the equation

x²-x-20=x+20-x-20 Simplify

x²-x-20=0 Factor

(x-5)(x+4)=0 Set each factor equal to zero and solve

x-5=0 Add 5 to both sides

x=5

x+4=0 Subtract 4 from both sides

x=-4

Answer 3

f(x) = g(x)

x² = x + 20

x² - x - 20 = 0

(x - 5)(x + 4) = 0

-4, 5