Graph y=12x-6x^2

Problem

y=12*x−6*x^2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x^2+b*x+c where a=−6 b=12 and c=0 Since a<0 the parabola opens downward.

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

0=6*x*(2−x)

x=0,x=2

3. Find the vertex by calculating the x-coordinate using x=(−b)/(2*a)

x=(−12)/(2*(−6))=1

4. Calculate the y-coordinate of the vertex by substituting x=1 into the original equation.

y=12*(1)−6*(1)^2=6

The vertex is at (1,6)

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

y=12*(0)−6*(0)^2=0

The y-intercept is (0,0)

6. Sketch the graph by plotting the vertex (1,6) the x-intercepts (0,0) and (2,0) and drawing a downward-opening parabola through these points.

Final Answer

y=−6*x^2+12*x

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