Graph y=x^2-6x+5

Problem

y=x2−6*x+5

Solution

1. Identify the type of function and its orientation. This is a quadratic function in the form y=a*x2+b*x+c Since a=1 which is positive, the parabola opens upward.

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

x=(−(−6))/(2*(1))

x=3

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

y=(3)2−6*(3)+5

y=9−18+5

y=−4

The vertex is (3,−4)

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

y=(0)2−6*(0)+5

y=5

The y-intercept is (0,5)

5. Find the x-intercepts by setting y=0 and factoring the quadratic.

x2−6*x+5=0

(x−1)*(x−5)=0

x=1,x=5

The x-intercepts are (1,0) and (5,0)

6. Plot the points and draw a smooth curve. Use the vertex (3,−4) the intercepts (0,5) (1,0) (5,0) and the axis of symmetry x=3 to complete the graph.

Final Answer

y=x2−6*x+5

The graph is an upward-opening parabola with vertex (3,−4) y-intercept (0,5) and x-intercepts (1,0) and (5,0)

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