Four possible sketches of $y = ax^2 + bx + c$ are shown below - AQA - A-Level Maths Pure - Question 1 - 2021 - Paper 2
Question 1
Four possible sketches of $y = ax^2 + bx + c$ are shown below.
Given $b^2 - 4ac = 0$ and $a$, $b$, and $c$ are non-zero constants, which sketch is the only one that... show full transcript
Worked Solution & Example Answer:Four possible sketches of $y = ax^2 + bx + c$ are shown below - AQA - A-Level Maths Pure - Question 1 - 2021 - Paper 2
Step 1
Given $b^2 - 4ac = 0$
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Answer
This equation indicates that the quadratic has a repeated root, meaning it touches the x-axis at one point and does not cross it. Therefore, the graph must be a parabola that opens either upwards or downwards but is tangent to the x-axis at that point.
Step 2
Analyzing the Sketches
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Answer
Looking at the sketches:
Sketch A: Opens downwards and has no x-axis intersection.
Sketch B: A parabola that opens upwards and has a single point of intersection with the x-axis, making it a valid candidate.
Sketch C: Opens upwards and crosses the x-axis at two points, which is incorrect.
Sketch D: Similar to C but opens downwards, which is also incorrect.
Thus, sketch B is the only one that could represent a quadratic with a repeated root.
Step 3
Final Answer
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