Everything Maths Grade 10

4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 0 (0;1) (2; 2) (2;4) 2 3 # +2! +3" x y Worked example 3: Sketching a straight line gra ...

Exercise 6 – 2: 1.Determine thex-intercept and they-intercept of the following equations. a) y=x 1 b)y=x+ 2 c) y=x 3 2.In the gr ...

8 6 4 2 2 4 6 8 8 6 4 2 2 4 6 8 (^61)  " . C x y a) y= 5 2 x b)x+ 5 c) y= 2x 6 d)y= 3 x e)y= 1 f) y=^12 x 8.For the fun ...

6.3 Quadratic functions EMA4H Functions of the formy=x^2 EMA4J Functions of the general formy=ax^2 +qare called parabolic functi ...

4 3 2 (^1) 1 1 2 3 4 1 2 3 4 5 6 7 8 9 10 0 (1; 1) (2; 4) (3; 9) (1; 1) (2; 4) (3; 9) B A x y Step 3: Determine the domain ...

Functions of the formy=ax^2 +q EMA4K Investigation: The effects ofaandqon a parabola. Complete the table and plot the following ...

a < 0 a > 0 q > 0 q= 0 q < 0 Table 6.2:The effect ofaandqon a parabola. VISIT: You can use thisPhet simulationto hel ...

SOLUTION Step 1: Determine the domain The domain isfx:x 2 Rgbecause there is no value for whichg(x)is undefined. Step 2: Determi ...

Sketching graphs of the formy=ax^2 +q EMA4N In order to sketch graphs of the formf(x) =ax^2 +q, we need to determine the followi ...

Worked example 7: Sketching a parabola QUESTION Sketch the graph ofg(x) =^12 x^2 3. Mark the intercepts and the turning point. ...

Exercise 6 – 3: 1.The graph below shows a quadratic function with the following form:y=ax^2 +q. Two points on the parabola are s ...

5.Given the following graph, identify a function that matches each of the following equations: 3 2 1 1 2 3 12 10 8 6 4 ...

g h 0 (0;9) (0;23) (4;7) (4;7) x y a)Find the values ofaandp. b)Find the values ofbandq. c)Find the values ofxfor whichg(x)h(x) ...

x 3 2 1 1 2 1 4 0 1 4 1 2 1 2 3 h(x) 1 3 1.Join the points with smooth curves. 2.What happens ifx= 0? 3.Explain why the gr ...

4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 0 h(x) =^1 x x h(x) Forx= 0the functionhis undefined. This is called a discontinuity atx ...

3.y 3 = 1 x 4.y 4 = 1 x + 1 5.y 5 = 1 x + 2 Use your results to deduce the effect ofq. On the same set of axes, plot the followi ...

Discovering the characteristics EMA4S The standard form of a hyperbola is the equationy= a x +q. Domain and range Fory= a x +q, ...

Thex-intercept: Every point on thex-axis has ay-coordinate of 0, therefore to calculate thex-intercept, lety= 0. For example, th ...

Step 2: Calculate the intercepts For they-intercept, letx= 0: g(x) = 2 x + 2 g(0) = 2 0 + 2 This is undefined, therefore there i ...

SOLUTION Step 1: Examine the standard form of the equation We see thata < 0 therefore the graph lies in the second and fourth ...