470 Chapter 8Graphing Quadratic Functions8
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Chapter ReviewGraphing f (x) = ax2 (pp. 419–424)8.1Graph g(x) 4x2. Compare the graph to the graph of f (x) x2.Step 1 Make a table of values.x21012g(x)1640416Step 2 Plot the ordered pairs.Step 3 Draw a smooth curve through the points. The graphs have the same vertex, (0, 0), and the same axis of symmetry, x 0, but the graph of g opens down and is narrower than the graph of f. So, the graph of g is a vertical stretch by afactor of 4 and a re ection in the x-axis of the graph of f.Graph the function. Compare the graph to the graph of f (x) = x2.1. p(x) 7x2 2. q(x) 1 — 2 x2 3. g(x) 3 — 4 x2 4. h(x) 6x25. Identify characteristics of the quadratic function and its graph.Graphing f (x) = ax2 c (pp. 425–430)8.2Graph g(x) 2x2 + 3. Compare the graph to the graph of f (x) x2.Step 1 Make a table of values.x21012g(x)1153511Step 2 Plot the ordered pairs.Step 3 Draw a smooth curve through the points. Both graphs open up and have the same axis of symmetry, x 0. The graph of g is narrower, and its vertex, (0, 3), is above the vertex of the graph of f, (0, 0). So, the graph of g is a vertical stretch by a factor of 2 and avertical translation 3 units up of the graph of f.Graph the function. Compare the graph to the graph of f (x) = x2.6. g(x) x2 + 5 7. h(x) x2 4 8. m(x) 2x2 + 6 9. n(x) 1 — 3 x2 58168x2424yf(x) x2g(x) 4x21313xy2261014x2424y14yg(x) 2x2 + 3f(x) x2Dynamic Solutionsavailable at BigIdeasMath.com