HOW DO YOU FIND THE AVERAGE RATE OF CHANGE USING THE GRAPH?

Mathematics

1 answer:

Rom4ik [11]3 years ago

8 0

Answer: Explained

Step-by-step explanation: We are to explain how to find the average rate of change using the graph.

In a graph, the average rate of change is given by the vertical change divided by the horizontal change between two points on a line.

Thus, the average rate of change is given by

$R=\dfrac{\textup{vertical change}}{\textup{horizontal change}}.$

In the attached figure, consider the points P(1.5,1) and Q(0,2).

So, vertical change = 2 - 1 = 1,

and

horizontal change = 0 - 1.5 = -1.5.

Therefore, rate of change is

$R=\dfrac{1}{-1.5}=-\dfrac{2}{3}.$

Hence, explained.

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For the function y=x^2-4x-5, perform the followingtasks:

lbvjy [14]

Answer:

a. $x^2-4x-5= \left(x-2\right)^2-9$ .

b. The axis of symmetry for ${\left(x - 2\right)^{2}} - 9$ is $x=2$ .

Step-by-step explanation:

a. The vertex form of a quadratic is given by $y=a(x-h)^2+k$ , where (h, k) is the vertex.

To convert from $y=x^2-4x-5$ form to vertex form you use the process of completing the square.

Step 1: Write $x^2-4x-5$ in the form $x^2+2ax+a^2$ . Add and subtract 4:

$x^{2} - 4 x - 5=x^{2} - 4 x + {\left(4\right)} - {4} - 5$

Step 2: Complete the square $x^2+2ax+a^2=\left(x+a\right)^2$

${\left(x^{2} - 4 x + 4\right)} - 9={\left(x - 2\right)^{2}} - 9$

b. The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.

For a quadratic function in standard form, $y=a(x-h)^2+k$ , the axis of symmetry is $x=h$ .