Dstermine the equation of function

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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.
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Azurin
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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.
 
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$y = a(x-h)^2 + k$

you are given $h = -1$

write two equations using the two given (x,y) coordinates and solve the system for $a$ and $k$
 
  • #3
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
 

Related to Dstermine the equation of function

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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