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A quadratic and a graph of it is given. A tangent is also sketched. The equation of the tangent line is asked for.

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The curve with equation \$y = \\simplify{{2}x^2+{2}x+{2}}\$ is sketched below.

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{plot(2,2,2,2, 14)}

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In addition, the tangent to the curve at \$x=2\$ has been drawn.

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(a) What is the gradient of the tagent at \$x=2\$? [[0]]

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(b) What is the \$y\$ coordinate at the point of contact between the tangent and the parabola? That is, what is the \$y\$ value when \$x=2\$? [[1]]

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(c) What is the equation of the tangent? \$y= \$[[2]]

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(d) \$L\$ is a horizontal straight line which is tangent to the curve. Determine the coordinates of where the line \$L\$ touches the curve. [[3]]

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example:

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