# Dstermine the equation of function

• MHB
• Azurin
In summary, to determine the equation of a quadratic function that passes through the points (0,3) and (-3,9) with an axis of symmetry at x=-1, we can use the equation y = a(x-h)^2 + k. With the given value of h=-1, we can create two equations using the two points and solve them for a and k. This will result in two possible equations, one with a positive value for a and one with a negative value, representing two different parabolas.
Azurin
The equation of the axis of symmetry of the graph of a quadratic function is x=-1. The graph passes through the points (0,3) and (-3, 9). Determine the equation of the function.

$y = a(x-h)^2 + k$

you are given $h = -1$

write two equations using the two given (x,y) coordinates and solve the system for $a$ and $k$

Azurin said:
The equation of the axis of symmetry of the graph of a quadratic function is x=-1. The graph passes through the points (0,3) and (-3, 9). Determine the equation of the function.
Actually, there are two solutions... one with a = A and one with a = -A. This corresponds to one parabola opening upward and another opening downward.

-Dan

## 1. What is the definition of a function?

A function is a mathematical relationship between two sets of values, where each input has only one corresponding output. It can be represented as an equation, table, or graph.

## 2. How do you determine the equation of a function?

To determine the equation of a function, you need to know the input and output values. You can use these values to create ordered pairs and then use these pairs to find the slope and y-intercept, which can be used to write the equation in slope-intercept form (y = mx + b).

## 3. What is the difference between linear and nonlinear functions?

A linear function has a constant rate of change and can be represented by a straight line on a graph. A nonlinear function does not have a constant rate of change and cannot be represented by a straight line on a graph.

## 4. How do you graph a function?

To graph a function, you can create a table of values by choosing different input values and plugging them into the equation. Then, plot these ordered pairs on a coordinate plane and connect them with a line to create the graph.

## 5. What is the purpose of finding the equation of a function?

Finding the equation of a function allows us to better understand and analyze the relationship between two sets of values. It also allows us to make predictions and solve problems related to the function.

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