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Four possible sketches of $y = ax^2 + bx + c$ are shown below - AQA - A-Level Maths Mechanics - 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 Mechanics - Question 1 - 2021 - Paper 2
Step 1
Given $b^2 - 4ac = 0$
Answer
The condition indicates that the quadratic has exactly one real root, meaning the graph must touch the x-axis at a single point. This implies that the parabola opens upwards if or downwards if , but must not cross the x-axis.
Out of the provided sketches:
- Sketch A: Crosses the x-axis twice - not valid.
- Sketch B: Touches x-axis once, is valid.
- Sketch C: Crosses the x-axis twice - not valid.
- Sketch D: Crosses the x-axis twice - not valid.
Thus, the only possible correct sketch is B.