Answer the whole of this question on a sheet of graph paper. The table below gives some $x$ and \(

Question

Answer the whole of this question on a sheet of graph paper. The table below gives some $x$ and $y$ values of the equation $y=-{{x}^{2}}-2x+5$. $x$ $-4$ $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $y$ $-3$ $2$ $5$ $6$ $5$ $2$ $-3$ $a$ Find the value of $a$. Taking $2$ cm to represent $1$ unit on the $x$-axis and $1$ cm to represent $1$ unit on the $y$-axis, draw the graph of $y=-{{x}^{2}}-2x+5$ for $-4\le x\le 3$. Use your graph to find the coordinates of the maximum point, the value of $y$ when $x=-1.5$, the values of $x$ when $y=4$, the equation of the line of symmetry. By drawing a suitable line, find the solutions to the equations $-{{x}^{2}}-2x-3=0$, $-{{x}^{2}}-x+7=0$.

Accepted Answer

(a) $a=-10$ (b) Graph shown in working (c)(i) $(-1,6)$ (ii) $y\approx5.8$ (iii) $x\approx-2.41$ or $0.41$ (iv) $x=-1$ (d)(i) No real solutions (ii) $x\approx-3.19$ or $2.19$

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically

Solution:

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