Graph f(x)=x^2-8x+15

Problem

ƒ(x)=x2−8*x+15

Solution

1. Identify the function type and its coefficients. This is a quadratic function in the form ƒ(x)=a*x2+b*x+c where a=1 b=−8 and c=15 Since a>0 the parabola opens upward.

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

x=(−(−8))/(2*(1))=4

Substitute x=4 into the function to find the ycoordinate:

ƒ(4)=(4)2−8*(4)+15=16−32+15=−1

The vertex is (4,−1)

3. Determine the y-intercept by evaluating ƒ(0)

ƒ(0)=0−8*(0)+15=15

The yintercept is (0,15)

4. Find the x-intercepts by setting ƒ(x)=0 and factoring the quadratic.

x2−8*x+15=0

(x−3)*(x−5)=0

The xintercepts are (3,0) and (5,0)

5. Plot the points and draw the parabola. Use the vertex (4,−1) the xintercepts (3,0) and (5,0) and the yintercept (0,15) to sketch the curve.

Final Answer

ƒ(x)=(x−4)2−1

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