Given the equation:
Let's find the x-intercepts and the y-intercepts of the graph.
• x-intercept:
The x-intercept are the points where the parabola crosses the x-axis. At x-intercept the y-value is zero.
To find the x-intercepts, substitute 0 for y and solve for x.
We have:
Rewrite the equation:
Factor the left hand side of the equation:
Equate each factor to zero:
x - 3 = 0
Add 3 to both sides:
x - 3 + 3 = 0 + 3
x = 3
x + 2 = 0
Subtract 2 from both sides:
x + 2 - 2 = 0 - 2
x = -2
Therefore, the x-intercepts are:
3, -2
• y-intercept:
The y-intercept is the point where the parabola crosses the y-axis. The x-value at the y-intercept is zero.
To find the y-intercept, substitute 0 for x and solve:
Therefore, the y-intercept is -6.
In point form:
x-intercept: (3, 0), (-2, 0)
y-intercept: (0, -6)
ANSWER:
A. The x-intercepts are (3, 0), (-2, 0)
A. The y-intercept is (0, -6)