How do you find an equation of a quadratic function from two points. The two points are the vertex and the y intercept.
Suppose you have y=ax^2 + bx + c
The vertex occurs when x satisifes 2ax+b=0 or x=-b/(2a)
The y intercept occurs at x=0, so it's the c component.
Do you have a specific problem you're solving?
To find the equation of a quadratic function when given the vertex and the y-intercept, you can follow these steps:
Step 1: Determine the vertex coordinates
The vertex of a quadratic function is in the form (h, k). In this case, you have the vertex coordinates, so assign them to (h, k). Use the vertex coordinates to find the values of a, b, and c.
Step 2: Substitute the vertex coordinates into the quadratic function equation
Replace the x and y variables in the equation with the values of the vertex coordinates. This will give you one equation with three variables: a, b, and c.
Step 3: Substitute the y-intercept into the equation
Since the y-intercept occurs when x = 0, substitute this value into the equation. This will give you a second equation with three variables: a, b, and c.
Step 4: Solve the system of equations
You now have a system of two equations with three variables. Solve the system to find the values of a, b, and c.
Step 5: Write the equation of the quadratic function
Once you have the values of a, b, and c, substitute them back into the quadratic function equation y = ax^2 + bx + c. This will give you the equation of the quadratic function.
If you have a specific problem you need help with, please provide the vertex coordinates and the y-intercept, and I can guide you through the steps using your specific values.