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