## Exam-Style Question on Quadratic Graph## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 586. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is not allowed.

Consider the function \(f(x)=\frac{1}{2}\left(2x-3\right)\left(x+5\right)\) for \(x \in \mathbb R\). The following diagram shows part of the graph of \(f\).

For the graph of \(f\)

(a) find the coordinates of the x-intercepts.

(b) find the coordinates of the vertex.

The function \(f\) can be written in the form \(f(x) = (x+h)^2 + k\)

(c) Write down the value of \(h\) and the value of \(k\).

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