Graph y=x^2-5x+6

Problem

y=x2−5*x+6

Solution

1. Identify the type of function. The equation is a quadratic function in the form y=a*x2+b*x+c which represents a parabola opening upward since a=1

2. Find the y-intercept. Set x=0 to find the point where the graph crosses the y-axis.

y=0−5*(0)+6

y=6

3. Find the x-intercepts. Set y=0 and factor the quadratic equation to find the roots.

x2−5*x+6=0

(x−2)*(x−3)=0

x=2,x=3

4. Find the vertex. Calculate the x-coordinate using x=(−b)/(2*a) and substitute it back into the equation to find the y-coordinate.

x=(−(−5))/(2*(1))=2.5

y=(2.5)2−5*(2.5)+6

y=6.25−12.5+6=−0.25

5. Plot the points. Use the vertex (2.5,−0.25) the x-intercepts (2,0) and (3,0) and the y-intercept (0,6) to sketch the parabola.

Final Answer

y=x2−5*x+6

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