what does this question mean :
Sketch a graph to show four graphs in each family.
a) y=(x-3)(x+6)
b) y= (x+1)(x+1)
dunno - what is a family of graphs?
enter your functions in the box at wolframalpha.com and it will show the graphs. Then you can play around with different parameters.
ok thanks
This question is asking you to sketch a graph for each of the given equations. It specifically mentions that there are four graphs in each family. The term "family" refers to the equations that have a similar structure or form. In this case, equation (a) and equation (b) are considered as two different families.
To sketch a graph for each equation, you will follow these steps:
1. Identify the type of equation: In both cases, the given equations are quadratic equations in the form of y = ax^2 + bx + c.
2. Find the vertex: The vertex of a quadratic equation in the form y = ax^2 + bx + c can be found using the formula x = -b/2a. In equation (a), the vertex can be found by substituting a = 1, b = -3, and c = 6 into the formula. In equation (b), the vertex can be found by substituting a = 1, b = 2, and c = 1 into the formula.
3. Determine the direction of the curve: Based on the value of 'a' in each equation, you can determine whether the quadratic curve opens upward or downward. If 'a' is positive, the curve opens upward, and if 'a' is negative, the curve opens downward.
4. Plot points: To plot the graph, you can substitute different values of 'x' into the equation and calculate the corresponding 'y' values. Start by finding the y-intercept, which is the value of 'y' when 'x' is zero. Then, choose other values for 'x' and calculate 'y' to find additional points.
5. Sketch the graph: Once you have multiple points, use a ruler or freehand drawing to connect the dots and create a smooth curve. Consider the direction (upward or downward) and the shape of the curve based on the value of 'a'.
Following these steps, you can sketch a graph for equation (a) and equation (b), and have four graphs in each family.