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mathematics UK Year 10 Mathematics (KS4)

Solved problems for the chapter:

Graphs of functions

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Parabola

1. Characteristics of a parabola

2. Equation of the parabola

3. Equation of the parabola passing through the origin

3.1. The first form of the parabola

3.2. The second form of the parabola

3.3. The third form of the parabola

3.4. The fourth form of the parabola

4. Equation of parabola not passing through the origin

5. Forum

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Quadratic function

1. Formats of the quadratic function

1.1. General form and meaning of the leading coefficient a

1.2. Zero shape and zero square functions

1.3. Top shape and quadratic function themes

1.3.1. Specify the peak shape

1.3.2. Determining the apex shape by completing it to a perfect square

2. Draw a graph of a quadratic function (parabola)

2.1. Drawing a parabola based on a general shape

2.2. Drawing a parabola based on the vertex shape

3. Mutual position of parabola and line

4. Forum

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Function and its property for KS4

1. Dependent and independent variable

1.1. Domain of a function

1.2. Range

2. Presentation of the function

2.1. Function rules

2.2. Function tabulation

2.3. Arrow diagram

2.4. Function graph

3. The x-intercept and the y-intercept

3.1. X-intercept

3.2. Zeros of a polynomial

3.2.1. Even zeros

3.2.2. Odd Zeros

3.3. y-intercepts

4. Injectivity, surjectivity and bijectivity

4.1. Injective function

4.2. Surjective function

4.3. Bijective function

5. Forum

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Quadratic equation

1. General form of the quadratic equation

1.1. Simplifying quadratic equations

1.1.1. Example of simplifying a quadratic equation

1.1.2. Generalisation of simplifying quadratic equation

2. Solving quadratic equations

2.1. Case D> 0

2.2. Case D = 0

2.3. Case D < 0

2.4. Solving special forms of quadratic equations by factorisation

2.4.1. Case b = 0 (generalisation)

2.4.2. Case b = 0 (practical example)

2.4.3. Case c = 0 (generalisation)

2.4.4. Case c = 0 (example)

2.4.5. Case a = 1 (generalisation)

2.4.6. Case a = 1 (example)

3. Zero form of the quadratic equation

4. Forum

↓ Show theory [4] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:graphs_of_functions/5322/

Example 1.

Draw a graph of the parabola

Example 2.

What the relationship of the variables in the graph below and write down its equation.

Table shows the relationship between the variables x and y. Complete the table for other values. Then show the dependence with an equation and draw a graph.

x	1	2	3	4	5	6
y	3	4	5

Draw a graph of the parabola .

The price of organically grown apples cost . Draw a graph of apple prices for masses , , .

Draw the graph of the function

Draw a graph of the parabola .

For the dependence of the variables x and y, which are related to the equation , complete the table and show their dependence with a graph.

x	y
-1
0
1

Draw a graph of the parabola .

10.

Draw a graph showing the dependence of the perimeter of a square on the length of its sides. The lengths of the sides of three squares are: , and .

11.

Draw the graph of the parabola .

12.

For the given values of x calculate the value of the function .

x	-5	-4	-3	-2	-1	0	1	2	3	4	5

13.

For the given statement, write the dependence of the variables x and y in the form of an equation.

Tina Maze overtook second-placed Mikaela Shiffrin by 0.10 seconds.
In Piran Bay, the sea level was higher than the water level at low tide when at high tide.

14.

The dependence of the variables x and y is given by the equation:

Which table does not show the dependencies of the variables x and y:

15.

Which table shows the dependence of the perimeter P of an equilateral triangle with side a?

Length a Perimeter P
Length a Perimeter P

16.

Complete the table showing the relationship between the sides of a triangle and its perimeter P.

Side a	Side b	Side c	Perimeter P
3	4	5
6.3	5.8		17
			1
		1	4

17.

Write the dependence of two quantities in the given text with the equation.

Nick is Lilian's younger sister. The age difference between them is years.

18.

Jure spent units on his mobile phone in January. The mobile operator charges for each unit, so he paid for the January payment slip. Write down which two variables are interdependent? Specifies the dependent and independent variable. Explain your answer.

19.

A parabola and a straight line are stated below:

Calculate the coordinates of the intersections of the parabola and the line.
Accurately draw the parabola and the line in the same coordinate system.
Calculate the angle that the line makes with the abscissa axis. Write the angle in degrees and minutes.

20.

Jana covers a distance of two kilometers in ten minutes. Write down which two variables are interdependent? Specifies the dependent and independent variable. Explain your answer.