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 cou... 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 $b^2 - 4ac = 0$, identify the condition for the quadratic equation.
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Answer
The condition b2−4ac=0 indicates that the quadratic has a double root. This means the graph of the quadratic equation touches the x-axis at exactly one point, creating a
Step 2
Evaluate the sketches provided.
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Answer
Out of the sketches A, B, C, and D:
Sketch A opens upwards and intersects the x-axis at one point (double root).
Sketch B does not intersect the x-axis.
Sketch C intersects the x-axis at two points.
Sketch D also intersects at two points.
Only Sketch A satisfies the condition for a double root.
Step 3
Select the correct sketch.
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Answer
Thus, the only sketch that could possibly be correct is:
