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 $y=-2{{x}^{2}}+x+8$. $x$ $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $y$ $-13$ $-2$ $p$ $8$ $7$ $2$ $-7$ Find the value of $p$. Using a scale of $2$ cm to represent $1$ unit, draw a horizontal $x$-axis for $-3\le x\le 3$ and a scale of $2$ cm to represent $5$ units, draw a vertical $y$-axis for $-15\le y\le 10$. On your axes, plot the points given in the table and join them with a smooth curve. Using your graph, find the maximum value of the curve, find the values of $x$ when $y=1$, solve the equation $-2{{x}^{2}}+x+8=0$, find the solutions of the equation $-2{{x}^{2}}+x+3=0$ by drawing a suitable straight line on the same axes. By drawing a suitable tangent, find the gradient of the graph at the point where $x=0$.

Accepted Answer

(a) $p=5$ (b) Graph shown in working (c)(i) $y\approx8.1$ (ii) $x\approx-1.64$ or $2.14$ (iii) $x\approx-1.77$ or $2.27$ (iv) $x\approx-1$ or $1.5$ (d) Gradient approximately $1$.

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically

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