Answer the whole of this question on a sheet of graph paper. The variables $x$ and $y$ are conne

Question

Answer the whole of this question on a sheet of graph paper. The variables $x$ and $y$ are connected by the equation $y=2{{x}^{2}}-5x-3$. Some corresponding values of $x$ and $y$ are given in the following table $x$ $-2$ $-1$ $0$ $0.5$ $1$ $2$ $3$ $4$ $5$ $6$ $y$ $p$ $4$ $-3$ $-5$ $-6$ $-5$ $0$ $9$ $22$ $39$ Calculate the value of $p$. Using $2$ cm to represent $1$ unit on the horizontal $x$-axis and $2$ cm to represent $5$ units on the vertical $y$-axis, draw the graph of $y=2{{x}^{2}}-5x-3$ for $-2\le x\le 6$. From your graph, find the minimum value of $y$. By adding suitable line to the graph on the same axes, find the solutions for the equation $2{{x}^{2}}-5x-3=10.$ On the same axis, draw the graph of the straight line $y+x=-1$. Write down the values of $x$ where the graphs$y=2{{x}^{2}}-5x-3$ and $y+x=-1$ intersect. This value of $x$ is a solution to the equation$a{{x}^{2}}+bx+c=0$. Find the value of $a,b$ and $c$.

Accepted Answer

(a) $p=15$ (b) Graph shown in working (c) $y\approx-6.1$ (d) $x\approx-1.59$ or $4.09$ (e)(i) $y=-x-1$, drawn in working (ii) $x\approx-0.41$ or $2.41$ (iii) One valid choice: $a=2,\;b=-4,\;c=-2$.

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically

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