Topic
Given the function \(y = a{x^2} + bx + c\) with the graph in Figure 11. Determine the sign \(a,b,c\)
Solution method – See details
We have the parabola \(y = a{x^2} + bx + c\) with vertices \(\left( {\frac{{ – b}}{{2a}}; – \frac{\Delta }{{ –) 4a}}} \right)\) and the line’s symmetry axis \(x = – \frac{b}{{2a}}\)
Detailed explanation
+ Parabola with downward concave surface \( \Rightarrow a < 0\)
+ Parabola intersects the vertical axis at the point (0;c) above the horizontal axis, so \(c > 0\)
+ The vertex is located to the right of the vertical axis, so it has a positive coordinate or \(x = \frac{{ – b}}{{2a}} > 0\), where \(a < 0 \Rightarrow b > 0\)
