Find the x and y Intercepts f(x)=-7x^2+6x+2

Problem

ƒ(x)=−7*x2+6*x+2

Solution

1. Find the y-intercept by setting x=0 and evaluating ƒ(0)

ƒ(0)=−7*(0)2+6*(0)+2

ƒ(0)=2

2. Find the x-intercepts by setting ƒ(x)=0 and solving the quadratic equation −7*x2+6*x+2=0

−7*x2+6*x+2=0

3. Apply the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a) where a=−7 b=6 and c=2

x=(−6±√(,6−4*(−7)*(2)))/(2*(−7))

4. Simplify the discriminant inside the square root.

x=(−6±√(,36+56))/(−14)

x=(−6±√(,92))/(−14)

5. Simplify the radical by factoring out the largest perfect square.

√(,92)=√(,4⋅23)=2√(,23)

x=(−6±2√(,23))/(−14)

6. Divide by the common factor of 2 to find the exact x-intercepts.

x=(−3±√(,23))/(−7)

x=(3∓√(,23))/7

Final Answer

y-intercept: *(0,2), x-intercepts: *((3−√(,23))/7,0),((3+√(,23))/7,0)

Want more problems? Check here!