Asked by junior
A student draws two parabolas on graph paper. Both parabolas cross the x-axis at (–4, 0) and (6, 0). The y-intercept of the first parabola is (0, –12). The y-intercept of the second parabola is (0, –24). What is the positive difference between the a values for the two functions that describe the parabolas? Write your answer as a decimal rounded to the nearest tenth.
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Both parabolas have zeros at x = −4 and x = 6, so each can be written y = a(x + 4)(x − 6). At x = 0, y = a(4)(−6) = −24a.
For the first parabola: −24a1 = −12 → a1 = 0.5.
For the second: −24a2 = −24 → a2 = 1.
Positive difference = |1 − 0.5| = 0.5. Rounded to the nearest tenth: 0.5.
For the first parabola: −24a1 = −12 → a1 = 0.5.
For the second: −24a2 = −24 → a2 = 1.
Positive difference = |1 − 0.5| = 0.5. Rounded to the nearest tenth: 0.5.
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