Put the quadratic into vertex form and state the coordinates of the vertex
y=x^2-4x-5
Vertex form:y=___________
Vertex:(,)
To put the quadratic equation into vertex form, we need to complete the square. The vertex form of a quadratic equation is given by:
y = a(x-h)^2 + k
Where (h, k) represents the coordinates of the vertex.
To complete the square, we take half of the coefficient of x (-4 in this case), square it (16), and add it to both sides of the equation:
y = x^2 - 4x - 5
y + 5 = x^2 - 4x + 16
We can rewrite the right side of the equation as a perfect square trinomial:
y + 5 = (x - 2)^2
To isolate y, we subtract 5 from both sides:
y = (x - 2)^2 - 5
Now we have the quadratic equation in vertex form. The coordinates of the vertex are (2, -5).
Vertex form: y = (x - 2)^2 - 5
Vertex: (2, -5)