For the quadratic equation, state the axis of symmetry, vertex, and any intercepts.
y = x2 − 4x − 5

Axis of Symmetry is x = 2

Vertex is (2, -9)

X Intercepts are (5, 0) and (-1, 0)

Step-by-step explanation:

Quadratic Equation is in standard form. Formula find the x value of the vertex in standard form is -b/2a

a=1

b=-4

c=-5

--4/2(1) = 2

Plugin to find the y value of the vertex.

2^2-4(2)-5=y

4-8-5=y

y = -9

The x value of the vertex (in this case is 2) is the axis of symmetry. Therefore the axis of symmetry is x=2

Factor the equation to put into intercept form.

(x-5)(x+1) = y

The equation can be FOIL-ed to get back to standard form.

Separate the 2 parentheses and whatever can cancel the parentheses are your intercepts.

For (x-5) your intercept is (5, 0)

For (x+1) your intercept is (-1, 0)

The x intercepts are where the parabola will cross the x axis on the graph.