# Exam-Style Questions on Quadratic Graphs

## Problems on Quadratic Graphs adapted from questions set in previous Mathematics exams.

### 1.

IB Standard

A function is defined as $$f(x) = 2{(x - 3)^2} - 5$$ .

(a) Show that $$f(x) = 2{x^2} - 12x + 13$$.

(b) Write down the equation of the axis of symmetry of this graph.

(c) Find the coordinates of the vertex of the graph of $$f(x)$$.

(d) Write down the y-intercept.

(e) Make a sketch the graph of $$f(x)$$.

Let $$g(x) = {x^2}$$. The graph of $$f(x)$$ may be obtained from the graph of $$g(x)$$ by the two transformations:

• a stretch of scale factor $$s$$ in the y-direction;
• followed by a translation of $$\left( {\begin{array}{*{20}{c}} j\\ k \end{array}} \right)$$ .

(f) Find the values of $$j$$, $$k$$ and $$s$$.

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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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