Graph y=x^2-4x

Problem

y=x2−4*x

Solution

1. Identify the type of function and its basic shape. The equation y=x2−4*x is a quadratic function in the form y=a*x2+b*x+c where a=1 b=−4 and c=0 Since a>0 the graph is a parabola that opens upward.

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

x=−(−4)/(2*(1))

x=2

3. Find the y-coordinate of the vertex by substituting x=2 into the original equation.

y=(2)2−4*(2)

y=4−8

y=−4

The vertex is at (2,−4)

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

0=x*(x−4)

x=0

x=4

The x-intercepts are (0,0) and (4,0)

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

y=(0)2−4*(0)

y=0

The y-intercept is (0,0)

6. Plot the points and draw a smooth curve. Use the vertex (2,−4) the intercepts (0,0) and (4,0) and additional points like (1,−3) and (3,−3) to sketch the parabola.

Final Answer

y=x2−4*x

The graph is a parabola opening upward with vertex (2,−4) and x-intercepts at x=0 and x=4

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