Question Video: Given the 𝑥-Intercepts and 𝑦-Intercepts Identify the Graph of a Quadratic Function Mathematics • Third Year of Preparatory School

Video Transcript

Which of the following graphs represents the quadratic function that intersects the 𝑥-axis at 𝑥 one equals negative one, 𝑥 two equals one and the 𝑦-axis at 𝑦 equals one?

We’re looking for a quadratic that intersects the 𝑥-axis at two points and the 𝑦-axis at one point. 𝑥-intercepts are located at some point 𝑥, zero. That is the place where the 𝑦-value of your coordinate equals zero. And similarly, the 𝑦-intercepts will be located at some point zero, 𝑦, where the 𝑥-value of the coordinate is equal to zero. Using the given information, we can then say the 𝑥-intercepts will be located at the point negative one, zero and one, zero. And the 𝑦-intercepts will be located at the point zero, negative one.

By graphing the 𝑥-intercepts, we can eliminate options (B), (C), and (E). The graphs in (A) and (D) both have 𝑥-intercepts at negative one, zero and one, zero. If we add the point zero, negative one, if we add the 𝑦-intercept, to these graphs, we can further eliminate option (D). Option (A) graphs the quadratic function with 𝑥-intercepts at 𝑥 equals negative one and 𝑥 equals one and a 𝑦-intercept at 𝑦 equals negative one.