Graph y=x^2+4x-5

Problem

y=x2+4*x−5

Solution

1. Identify the coefficients of the quadratic equation in the form y=a*x2+b*x+c

a=1

b=4

c=−5

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)−5

y=4−8−5

y=−9

The vertex is (−2,−9)

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

y=0+4*(0)−5

y=−5

The y-intercept is (0,−5)

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

0=x2+4*x−5

0=(x+5)*(x−1)

x=−5

x=1

The x-intercepts are (−5,0) and (1,0)

6. Sketch the parabola using the vertex (−2,−9) the y-intercept (0,−5) and the x-intercepts (−5,0) and (1,0) Since a>0 the parabola opens upward.

Final Answer

y=x2+4*x−5

The graph is a parabola opening upward with vertex (−2,−9) y-intercept (0,−5) and x-intercepts (−5,0) and (1,0)

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