Question

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

Answer 1

To find the vertex, we can use the formula x = -b / (2a), where a = 1 and b = 2.

x = -2 / (2*1) = -2/2 = -1

Now we substitute x = -1 back into the equation to find y.

y = (-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -4

Therefore, the vertex is (-1, -4).

The axis of symmetry is the vertical line that passes through the vertex, which is x = -1.

To find the x-intercepts, we set y = 0 and solve for x.

0 = x^2 + 2x - 3

This is a quadratic equation that can be factored as:

0 = (x + 3)(x - 1)

Setting each factor equal to zero:

x + 3 = 0 --> x = -3

x - 1 = 0 --> x = 1

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

To find the y-intercept, we set x = 0 and solve for y.

y = (0)^2 + 2(0) - 3 = -3

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