Problem 10 · 2021 Math Kangaroo
Medium
Algebra & Patterns
evaluate-formulasubstitution
The parabola in the figure has an equation of the form \(y = ax^{2} + bx + c\) for some distinct real numbers a, b and c. Which of the following equations could be an equation of the line in the figure?
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Answer: D — \(y = ax + c\)
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Hint 1 of 2
The parabola opens upward, so what is the sign of a?
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Hint 2 of 2
Match the line's slope and y-intercept to combinations of a, b and c.
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Approach: read the sign of a and the intercept from the picture
- The parabola opens upward, so a > 0, giving a positive slope; its y-intercept is c.
- The line in the figure has positive slope and the same y-intercept c.
- An equation with slope a and intercept c is y = ax + c.
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