Graph f(x)=x^2+4

Problem

ƒ(x)=x2+4

Solution

1. Identify the type of function, which is a quadratic function in the form ƒ(x)=a*x2+c

2. Determine the vertex of the parabola by using the standard form ƒ(x)=a*(x−h)2+k where (h,k) is the vertex.

3. Calculate the vertex coordinates, which are (0,4) since h=0 and k=4

4. Find the y-intercept by evaluating ƒ(0) which results in ƒ(0)=0+4=4

5. Determine the direction of the opening; since the coefficient of x2 is positive (a=1, the parabola opens upward.

6. Plot additional points to define the shape, such as ƒ(1)=1+4=5 and ƒ*(−1)=(−1)2+4=5

7. Sketch the curve as a smooth U-shaped parabola passing through (0,4) (1,5) and (−1,5)

Final Answer

ƒ(x)=x2+4

Want more problems? Check here!