Graph y=x^2-2x

Problem

y=x2−2*x

Solution

1. Identify the type of function and its basic shape. The equation y=x2−2*x is a quadratic function in the form y=a*x2+b*x+c where a=1 b=−2 and c=0 Since a>0 the graph is a parabola that opens upward.

2. Find the vertex using the formula x=(−b)/(2*a)

x=(−(−2))/(2*(1))

x=1

Substitute x=1 into the original equation to find the ycoordinate:

y=(1)2−2*(1)

y=−1

The vertex is (1,−1)

3. Find the x-intercepts by setting y=0 and factoring the expression.

x2−2*x=0

x*(x−2)=0

x=0

x=2

The xintercepts are (0,0) and (2,0)

4. Find the y-intercept by setting x=0

y=(0)2−2*(0)

y=0

The yintercept is (0,0)

5. Plot the points and draw a smooth curve. Use the vertex (1,−1) the intercepts (0,0) and (2,0) and additional points like x=−1 (y=3 and x=3 (y=3 to define the parabola.

Final Answer

y=x2−2*x

The graph is an upward-opening parabola with vertex (1,−1) and xintercepts at (0,0) and (2,0)

Want more problems? Check here!