# f(x) = x^2+11x-5

## The parabola for this equation opens upward because in vertex form, a is positive.

## The vertex is located at -5.5, -35.25

I found the vertex using the vertex formula, a(x-h)^2+k, where x and y equal h and k respectively.

(11/2)^2 = (5.5)^2 = 30.25

x^2+11x+30.25-30.25-5

(x+5.5)^2-30.25-5

(x+5.5)^2-35.25

(11/2)^2 = (5.5)^2 = 30.25

x^2+11x+30.25-30.25-5

(x+5.5)^2-30.25-5

(x+5.5)^2-35.25

## The Axis of Symmetry is -5.5

I found the axis of symmetry using the vertex formula, a(x-h)^2+k, where h equals the x intercept.

(11/2)^2 = (5.5)^2 = 30.25

x^2+11x+30.25-30.25-5

(x+5.5)^2-30.25-5

(x+5.5)^2-35.25

(11/2)^2 = (5.5)^2 = 30.25

x^2+11x+30.25-30.25-5

(x+5.5)^2-30.25-5

(x+5.5)^2-35.25

## The minimum value is -35.25

I found the minimum value using the vertex formula, a(x-h)^2+k, where k equals the minimum value.

(11/2)^2 = (5.5)^2 = 30.25

x^2+11x+30.25-30.25-5

(x+5.5)^2-30.25-5

(x+5.5)^2-35.25

(11/2)^2 = (5.5)^2 = 30.25

x^2+11x+30.25-30.25-5

(x+5.5)^2-30.25-5

(x+5.5)^2-35.25

## The y-intercept is -5

I found the y-intercept by substituting 0 for x in the vertex form of the quadratic function.

(11/2)^2 = (5.5)^2 = 30.25

x^2+11x+30.25-30.25-5

(x+5.5)^2-30.25-5

(x+5.5)^2-35.25

(0+5.5)^2-35.25

5.5^2-35.25

30.25-35.25

-5

(11/2)^2 = (5.5)^2 = 30.25

x^2+11x+30.25-30.25-5

(x+5.5)^2-30.25-5

(x+5.5)^2-35.25

(0+5.5)^2-35.25

5.5^2-35.25

30.25-35.25

-5

## The x-intercepts are .44 and -11.44

I solved the equation by using the quadratic formula to find the x-intercepts.

x = -11 +-sqrt11^2-4(1)(-5) / 2(1)

x = -11 +-sqrt121-(-20) / 2

x = -11 +-sqrt141 / 2

x = -11 +-11.87 / 2

x = -5.5 +-5.935

x = 0.435 or x = -11.435

Additionally, because there are no like terms, this equation cannot be factored.

x = -11 +-sqrt11^2-4(1)(-5) / 2(1)

x = -11 +-sqrt121-(-20) / 2

x = -11 +-sqrt141 / 2

x = -11 +-11.87 / 2

x = -5.5 +-5.935

x = 0.435 or x = -11.435

Additionally, because there are no like terms, this equation cannot be factored.

## Other Points

I know immediately after finding the y-intercept that due to the reflective property of symmetry, the parabola intersects a point that is the same distance from the axis of symmetry. This point is -11, -5. Additionally, from looking at the graph, I can see that the parabola intersects point -10, -15 and another point from reflection across the axis of symmetry at -1,-15.

The curves of the letter m in McDonalds are parabolas. This McDonalds is located at 29 E Chelten Ave, Philadelphia, PA 19144. | The graph of the quadratic function with all points mentioned included. | The curve of the letter u in United is a parabola. This post office is located at 5209 Greene St, Philadelphia, PA 19144. |