In this Graph, the curved lines that connect each (x,y) coordinate is called Parabola. The turning point of a parabola is called the Vertex. From the vertex, the graph stops going up to go down; and vice versa. In the graph shown, the vertex is (0,0). Notice that the points are symmetric to eachother, this means that there is an Axis of Symmetry. The Axis of Symmetry is a vertical line that can be drawn through the vertex of the parabola. In this graph, the axis of symmetry is x=0. The Direction of Opening in this graph is very easy to determine. Since the graph is going upwards, the direction of opening is up. The Maximum or Minimum value is determined by its vertex and direction of opening. First, observe direction of opening. If it is going upwards, the graph has a minimum value; if it is going downwards, the graph has a maximum value.
When asked about the shape, there are 3 main descriptions : wide, basic, and narrow:
We are often given a formula when graphing a function.
In the Graph below, the formula of the function is : f(x)= x^2+1. Note that the “ f(x)” is the same thing as saying “y=x^2+1”.
When graphing a quadratic function, we could sketch it by using a table of values or remember its shape by the pattern it makes with its coordinates. ( 1,1, --2,4--3,9..) Since there is a “+1” written in the formula, this means that the coordinates go up by 1 from its original point.
(shown in the graph)
If you were to use a table of values, this is how it would look like ..
how to solve for y :
Y= (2)^2 +1 = 5
Y = (1)^2 +1 = 2
Y=
(0)^2 +1 =1
Y= (-1)^2+1 =2
Y= (-2)^2+1 =5
things to remember for f(x)=ax^2
- If the “a” value is positive; ie -> y= 3(-2)^2 = 12
- The direction of opening goes upwards.
- If the “a” value is negative; ie ->y= -3(-2)^2 =- 12
- the axis of symmetry is the y axis
- - if a>0 , the graph opens upwards and has a minimum
- -if a<0, the graph opens downwards and has a maximum.
- - the coordinates of the vertex are (0,0)
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