y=4
Step-by-step explanation:
f(x)=x⁴-5x²+4
y=x⁴-5x²+4
0=x⁴-5x²+4
1. Ask: Which two numbers add up to−5 andmultiply to 4?
−4 and -1
2. Rewrite the expression using the above.
•(x^2 −4)(x^2 −1)
•0=(x^2-4)(x^2-1)
3.Rewrite x^2 −4 in the form a^2-b^2 where a=x and b=2.
•0=(x^2 −2^2 )(x^2 −1)
4.Use Difference of Squares:a^2 −b^2 =(a+b)(a−b).
•0=(x+2)(x−2)(x^2 −1)
5.Rewrite x^2 −1 in the form a^2- b^2, where a= x and b= 1.
•0=(x+2)(x−2)(x^2 - 1^2 )
6 Use Difference of Squares:a^2 −b^2 =(a+b)(a−b).
•0=(x+2)(x−2)(x+1)(x−1)
7 Switch sides.
•(x+2)(x−2)(x+1)(x−1)=0
8.Solve for x.
1 Ask: When will (x+2)(x−2)(x+1)(x−1) equal zero?
•When x+2=0, x−2=0, x+1=0, or x−1=0
2 Solve each of the 4 equations above.
•x=±2,±1
2. y-Intercept
1 Let x=0 to find the y-intercept(s).
•y=0^4 −5×0^2+4
> y=0^4-5×0^2+4
1.x-Intercept
1.Let y=0 to find the x-intercept(s).
•0=0^4-5×0^2+4
2.Simplify 0^4 to 0.
•0=0-5 0^2+4
3.Simplify 0^2 2 to 0.
•0=0−5×0+4
4.Simplify 5×0 to 0.
•0=0-0+4
5.Simplify 0-0 to 0.
•0=0+4
6.Simplify 0+4 to 4.
•0=4
2. y-Intercept
1.Let x=0x=0 to find the y-intercept(s).
y=0^4−5×0^2+4
2.Simplify.
y=4
