The graph of a quadratic function has a y-intercept at (0, 3) and its vertex at (4,...
Check the final answer first, then review the worked steps.
Problem
The graph of a quadratic function has a y-intercept at (0, 3) and its vertex at (4, 8 1/3). What are its x-intercepts, in order from least to greatest?
Step-by-step solution
The vertex form of the quadratic function is $y = a(x-h)^2 + k$. Using the vertex $(4, 8\frac{1}{3})$ and y-intercept $(0, 3)$, we find $a = -1/12$. The function is $y = -1/12(x-4)^2 + 25/3$. Setting $y=0$ and solving for $x$ gives the x-intercepts.
Answer
4 +/- 2*sqrt(25/3)