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 $p$. Taking $2$ cm to represent $1$ unit on the $x$-axis and $2$ cm to represent $5$ units on the $y$-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 drawing a tangent, find the gradient of the curve at the point where $x=3$. By adding suitable line(s) on the same axes, find the solutions for the equation $2{{x}^{2}}-5x-3=10.$ the solutions for the equation $2{{x}^{2}}-6x-2=0.$ the range of values of $x$ for which $2{{x}^{2}}-5x-3<0.$

Accepted Answer

(a) $p=15$ (b) Graph shown in working (c) $y\approx-6.1$ (d) Gradient approximately $7$ (e)(i) $x\approx-1.59$ or $4.09$ (ii) $x\approx-0.30$ or $3.30$ (iii) $-0.5<x<3$.

Quadratic Functions, Equations and Inequalities - Quadratic Inequalities

Quadratic Functions, Equations and Inequalities - Quadratic Inequalities

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