GCSE Maths: Non-linear graphs flashcards

Question 1

What is a quadratic?

Accepted Answer

An equation, graph or sequence in which the highest exponent of the variable is 2.

Question 2

What is the general form of a quadratic?

Accepted Answer

ax² + bx + c

Question 3

Every point on a parabola is an equal distance from which two things?

Accepted Answer

A fixed point (the focus) and a fixed straight line (the directrix).

Question 4

When drawing a graph from its equation, what is a table of values useful for?

Accepted Answer

Identifying coordinate pairs that satisfy the equation.

Question 5

In a table of values, how do you find the y-value for each x-value?

Accepted Answer

Substitute the x-value into the equation to calculate the corresponding y-value.

Question 6

When drawing y = x², should the plotted points be joined with straight line segments?

Accepted Answer

No. For example, (1/2, 1/2) lies on the segment from (0, 0) to (1, 1) but does not satisfy y = x².

Question 7

What is the shape of a quadratic graph called?

Accepted Answer

A parabola.

Question 8

On the graph of an equation, where are the roots of the equation?

Accepted Answer

Where the graph intercepts the x-axis (where y = 0).

Question 9

What is the turning point of a graph?

Accepted Answer

A point on the curve where, as x increases, the y-values change from decreasing to increasing or from increasing to decreasing.

Question 10

What is the turning point of a quadratic graph?

Accepted Answer

The maximum or minimum point of the graph.

Question 11

What is a cubic?

Accepted Answer

An equation, graph or sequence in which the highest exponent of the variable is 3.

Question 12

When drawing y = x³, does the point (1/2, 1/2) on the segment from (0, 0) to (1, 1) lie on the graph?

Accepted Answer

No. (1/2, 1/2) does not satisfy y = x³, so the points should not be joined with straight line segments.

Question 13

What is the reciprocal of a non-zero number?

Accepted Answer

Its multiplicative inverse.

Question 14

What do you get when you multiply a non-zero number by its reciprocal?

Accepted Answer

1

Question 15

What type of graph is an inverse proportion graph?

Accepted Answer

A reciprocal graph.

Question 16

Does 1 ÷ 0 evaluate to 0?

Accepted Answer

No. Trying x = 1/2, 1/3, 1/4 and so on shows the y-axis acting as an asymptote of the reciprocal graph.

Question 17

When is the relationship between two variables linear?

Accepted Answer

When plotting it on a pair of axes forms a straight line.

Question 18

What can the shape of a graph be used to identify?

Accepted Answer

The form of its equation.

Question 19

If a graph has a context, how should its solutions be given?

Accepted Answer

In context.

Question 20

If a graph is drawn on axes with no scale, can anything be inferred about its equation?

Accepted Answer

Yes. Its shape (parabola, cubic or reciprocal) and features such as the signs of coefficients and the y-intercept tell you much about the equation.

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