Answer the whole of this question on a sheet of graph paper. The following table gives the correspon

Question

Answer the whole of this question on a sheet of graph paper. The following table gives the corresponding values of $x$ and $y$ which are connected by the equation $y={{x}^{2}}-2x-8$. $x$ $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $4$ $5$ $y$ $7$ $p$ $-5$ $-8$ $q$ $-8$ $-5$ $0$ $7$ Calculate the values of $p$ and $q$. Using a scale of $2$ cm to represent $1$ unit on the $x$-axis and $1$ cm to represent $1$ unit on the $y$-axis, draw the graph of $y={{x}^{2}}-2x-\mathrm{8}$ for $-3\le x\le 5$. Write down the equation of the line of symmetry. By drawing a suitable tangent, find the gradient of the graph at the point where $x=2$.

Accepted Answer

(a) $p=0,\;q=-9$ (b) Graph shown in working (c) $x=1$ (d) Gradient approximately $2$.

Quadratic Functions, Equations and Inequalities - Sketching Quadratic Graphs

Quadratic Functions, Equations and Inequalities - Sketching Quadratic Graphs

Solution:

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