// Numbas version: exam_results_page_options {"name": "Prerequisites: reading graph and symmetry", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": ["jsxgraph"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

A quadratic equation (equivalent to \$(x+a)^2-b\$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

See 4.1 for background on quadratics. See 1.1 for what solving means.

{plot(a,b)}

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Below is a graph. Note that it is symmetrical.

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(i) When the \$x\$-coordinate on the graph is \$\\var{x[1]}\$, what is the \$y\$-coordinate?  [[0]]

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(ii) When the \$x\$-coordinate on the graph is \$\\var{x[4]}\$, what is the \$y\$-coordinate? [[1]]

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(iii) When the \$y\$-coordinate on the graph is \$\\var{y[0]}\$, what is the \$x\$-coordinate? [[2]]

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(iv) When \$y=0\$, there are two possible \$x\$-coordinates. One of them is \$\\var{x'}\$.  By using the symmetry of the graph, determine the other possibility. Give your answer to 2 decimal places. [[3]]

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