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

Question

Answer the whole of this question on a sheet of graph paper. The table below gives some values of $x$ and the corresponding values of $y$ where$y=-{{x}^{2}}+2x+5$ for $-3\le x\le 5$. $x$ $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $4$ $5$ $y$ $-10$ $-3$ $2$ $5$ $p$ $5$ $2$ $-3$ $-10$ Calculate the value of $p$. 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 $y=-{{x}^{2}}+2x+5$. Use your graph to find the value of $y$ when $x=4.5$, maximum point. By drawing suitable line(s) to the graph, find the solution(s) to the equation $-{{x}^{2}}+x+6=0$ $-{{x}^{2}}+x+2=0$

Accepted Answer

(a) $p=6$ (b) Graph shown in working (c)(i) $y\approx-6.3$ (ii) $(1,6)$ (d)(i) Draw $y=x-1$: $x=-2$ or $3$ (ii) Draw $y=x+3$: $x=-1$ or $2$

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically

Solution:

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