Find the x and y Intercepts f(x)=5x^2+6

Problem

ƒ(x)=5*x2+6

Solution

1. Find the y-intercept by setting x=0 and evaluating the function.

ƒ(0)=5*(0)2+6

ƒ(0)=6

2. Identify the y-intercept as a point.

y-intercept=(0,6)

3. Find the x-intercepts by setting ƒ(x)=0 and solving for x

5*x2+6=0

4. Isolate the x-squared term by subtracting 6 from both sides.

5*x2=−6

5. Divide by the coefficient of the squared term.

x2=−6/5

6. Apply the square root property to solve for x

x=±√(,−6/5)

7. Determine the nature of the roots by observing that the square root of a negative number is not a real number.

x=±i√(,6/5)

8. Conclude the x-intercepts do not exist in the set of real numbers because the equation has no real solutions.

x-intercepts=None

Final Answer

y-intercept: *(0,6), x-intercepts: None

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