The variables $x$ and $y$ are connected by the equation $y = -x^2 + 2x + 3$. Some correspondin

Question

The variables $x$ and $y$ are connected by the equation $y = -x^2 + 2x + 3$. Some corresponding values of $x$ and $y$ are given in the table below. $x$$-2$$-1$$0$$1$$2$$3$$4$ $y$$-5$$a$$3$$4$$3$$0$$-5$ Calculate the value of $a$. [1] On the grid provided on the next page, plot the points given in the table and join them with a smooth curve. [3] Use your graph to find the values of $x$ when $y = 1.4$. [2] Write down the equation of the line of symmetry of the graph. [1] Using your graph, explain why $y = -x^2 + 2x + 3$ does not have any solution when $y = 5$. [1]

Accepted Answer

(a) $a=0$ (b) Plot:$(-2,-5),\ (-1,0),\ (0,3),\ (1,4),\ (2,3),\ (3,0),\ (4,-5)$. Join the points with a smooth curve. (c)$x\approx -0.6\text{ or } x\approx2.6$(d) $x=1$ (e) No real solution when $y=5$.

Algebraic Expressions, Identities and Formulae

Algebraic Expressions, Identities and Formulae

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