Graph the quadratic equation y = x^2 + x – 2.
Identify the axis of symmetry and the vertex.
To graph the quadratic equation y = x^2 + x - 2, we can start by plotting a few points on a coordinate plane and connecting them.
Let's choose some x-values and find the corresponding y-values using the equation:
When x = -3:
y = (-3)^2 + (-3) - 2 = 9 - 3 - 2 = 4
So, we have the point (-3, 4).
When x = -2:
y = (-2)^2 + (-2) - 2 = 4 - 2 - 2 = 0
So, we have the point (-2, 0).
When x = -1:
y = (-1)^2 + (-1) - 2 = 1 - 1 - 2 = -2
So, we have the point (-1, -2).
When x = 0:
y = (0)^2 + (0) - 2 = 0 - 2 = -2
So, we have the point (0, -2).
When x = 1:
y = (1)^2 + (1) - 2 = 1 + 1 - 2 = 0
So, we have the point (1, 0).
When x = 2:
y = (2)^2 + (2) - 2 = 4 + 2 - 2 = 4
So, we have the point (2, 4).
Now, we can plot these points on a coordinate plane and connect them to get a graph of the quadratic equation y = x^2 + x - 2.
To find the axis of symmetry, we use the formula x = -b / (2a). In this equation, a = 1, b = 1, and c = -2.
Axis of symmetry:
x = -b / (2a) = -1 / (2 * 1) = -1 / 2
So, the axis of symmetry is x = -1/2.
To find the vertex, we substitute the axis of symmetry value into the equation.
x = -1/2:
y = (-1/2)^2 + (-1/2) - 2 = 1/4 - 1/2 - 2 = -15/4
So, the vertex is (-1/2, -15/4).
Plotting the axis of symmetry and the vertex on the graph, we obtain the following quadratic graph:
well, note that
x^2 + x - 2 = (x + 1/2)^2 - 9/4
It's not called the vertex form for nothing ...