Question

Determine the vertex, axis of symmetry, x-intercept, and y -intercept for the equation: y=x2+2x−3
.

Answer 1

The vertex form of the equation is y = a(x-h)^2 + k, where (h, k) is the vertex.

For the equation y = x^2 + 2x - 3:
a = 1
h = -1 (opposite sign of x-coefficient and divided by 2)
k = (-1)^2 + 2(-1) - 3 = -2

So the vertex is (-1, -2).

The axis of symmetry is given by the equation x = -h, so x = 1.

To find the x-intercepts, set y = 0 and solve for x:
0 = x^2 + 2x - 3
0 = (x+3)(x-1)
x = -3 or x = 1

The x-intercepts are (-3, 0) and (1, 0).

To find the y-intercept, set x = 0:
y = (0)^2 + 2(0) - 3
y = -3

So the y-intercept is (0, -3).