AQA · Mathematics · 8300
GCSE Maths: Quadratic graphs: drawing
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise, practice questions and answers for Quadratic graphs: drawing (Corbettmaths Video 264), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the general shape of a quadratic graph?
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A parabola (a U-shaped curve).
The graph of y = x² + 3 is a vertical ? of y = x².
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translation
How does the coefficient of x² affect the shape of a quadratic graph?
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A larger coefficient makes the parabola narrower (steeper); a smaller coefficient makes it wider.
A quadratic graph of the form y = ax² where a > 0 has a ? point.
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minimum
What happens to the graph of y = x² when you replace it with y = 8 − x²?
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The parabola flips upside down (opens downward) and is shifted up by 8 units.
The line of symmetry of a quadratic graph passes through its ?.
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vertex
For the quadratic y = x² − 5x + 4, what does the line of symmetry represent?
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A vertical line that divides the parabola into two mirror-image halves.
What method is commonly used to draw a quadratic graph accurately?
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Create a table of values by substituting x values into the equation, then plot the resulting (x, y) points.
How many points do the roots of a quadratic represent on its graph?
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The points where the graph crosses the x-axis (where y = 0).
For y = 4 - x², what is the value of y when x = 1?
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3. Because 4 - 1² = 4 - 1 = 3.
For y = 4 - x², what is the value of y when x = -3?
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-5. Because 4 - (-3)² = 4 - 9 = -5.
For y = 4 - x², what is the value of y when x = 2?
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0. Because 4 - 2² = 4 - 4 = 0.
For the quadratic equation y = 4 - x², what is the maximum value of y?
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4. This occurs when x = 0, because x² is always non-negative.
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