When the quadratic function $f$ is graphed in the $xy$-plane, where $y=f(x)$, its vertex $(2, -3)$ is 5 units away from the $x$-intercepts of the graph. Which equation defines $f$?
Answer:
C
Explanation
The correct answer is Choice C.
Draw the graph and locate the $x$-intercept knowing that a quadratic function is symmetrical along the vertical line that goes through the vertex of the graph.
Choice A is incorrect and may result from switching the $x$ and $y$ coordinate of the vertex.
Choice B is incorrect and may result from algebraic mistakes when finding the lead coefficient.
Choice D is incorrect and may result from sign error when writing the function in the $x$-intercept form.
✨ Expert's Tip ✨
A graph of a quadratic function is symmetric along the vertical line that goes through the vertex. Therefore, the vertex is at the middle of the two $x$-intercepts.