Graph f(x)=a(x-h)^2+k

Problem

ƒ(x)=a*(x−h)2+k

Solution

1. Identify the vertex of the parabola by looking at the constants h and k The vertex is located at the point (h,k)

2. Determine the direction of opening by checking the sign of the coefficient a If a>0 the parabola opens upward. If a<0 the parabola opens downward.

3. Determine the vertical stretch or compression based on the absolute value of a If |a|>1 the graph is narrower than the parent function y=x2 If 0<|a|<1 the graph is wider.

4. Find the axis of symmetry, which is the vertical line passing through the vertex. The equation for this line is x=h

5. Calculate additional points to ensure accuracy. A common method is to find the yintercept by evaluating ƒ(0) and finding the xintercepts by solving ƒ(x)=0

6. Plot the points on a coordinate plane and draw a smooth, U-shaped curve (parabola) through them, ensuring it is symmetric about the line x=h

Final Answer

ƒ(x)=a(x−h)+k* is a parabola with vertex *(h,k)

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