iGCSE (2021 Edition)

Consider a parabola of the form $y=ax^2+bx+c$`y`=`a``x`2+`b``x`+`c`, where $a>0$`a`>0

a

Which of the following statements is true?

The vertex of the parabola is a maximum point.

A

The vertex of the parabola is a minimum point.

B

The vertex of the parabola is a maximum point.

A

The vertex of the parabola is a minimum point.

B

b

Each parabola below has an equation of the form $y=ax^2+bx+c$`y`=`a``x`2+`b``x`+`c`.

Select all the graphs for which $a>0$`a`>0

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A

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B

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C

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D

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A

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B

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C

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D

Easy

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Find the maximum or minimum value of the quadratic function f : x ↦ ax^2 + bx + c by any method.

Use the maximum or minimum value of f(x) to sketch the graph or determine the range for a given domain.

Know the conditions for f(x) = 0 to have two real roots, two equal roots, no real roots. Know the related conditions for a given line to intersect a given curve, be a tangent to a given curve, not intersect a given curve.