// Numbas version: exam_results_page_options {"name": "Differentiation: Equation of tangent. Quadratic", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Differentiation: Equation of tangent. Quadratic", "statement": "

This is a calculator question.

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

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{plot(a,b,c,x, fx)}

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

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(a) What is the equation of the tangent? \$y= \$  [[0]]

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

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[[1]]

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

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See Lecture 9.4 and Workshop 9.5 for the background and examples.

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If you're unsure on equation of straight lines, go to Week 4 of Maths 1. Look at the lectures, workshops and/or CLEs.

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(a) Similar questions are in Lecture 9.4 and Workshop 9.5.

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(b) There is not an example like (b) in the lectures or workshops. You will have to think for yourself. Some hints:

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-- What does the information provided tell us about the gradient of the line.

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-- Once you know the gradient of the line, you have to find the appropriate value of \$x\$ which achieves this gradient.

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