Description
An equation and its graph are given. Find the x- and y-intercepts. (If an answer does not exist, enter DNE.)
y = 3x − x2
| x-intercepts | (x, y) = ( ) | (smaller x-value) |
(x, y) = ( ) | (larger x-value) | |
| y-intercept | (x, y) = ( ) |
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Explanation & Answer
Without looking at the graph, you can plug in 0 for x to find the y-intercept. This gives you y = 3(0) - (0)^2, which simplifies to 0.
Without the graph, you can factor out a greatest common factor (GCF) to get y = x(3-x). Then you can set each factor equal to 0 and solve the equations. You get 0 = x and 0 = 3 - x. The first one automatically gives you x = 0 as one of the x-intercepts and the you can solve the second one by adding x to both sides to get x=3 as the second x-intercept.
To write this in coordinate form, y = 0 at the x-intercept and x = 0 at the y-intercept. This means you will have x-intercepts at (0,0) and (3,0) and a y-intercept at (0,0).
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