Final answer:
To find the vertex form of a quadratic equation using a calculator, substitute the given vertex and another point into the vertex form and solve for 'a'. This yields the complete equation in vertex form.
Step-by-step explanation:
To find the vertex form of a quadratic equation given the vertex and another point using a calculator, you need to follow several steps. The vertex form of a quadratic equation is y = a(x - h)² + k where (h,k) is the vertex of the parabola.
Steps to Find the Vertex Form:
- First, identify the vertex (h,k) of the parabola. This is given to you as part of the problem.
- Take another point (x, y) that lies on the parabola. This point is also typically provided in the problem.
- Substitute the vertex and the point into the vertex form equation to create two equations with the unknown 'a'.
- Use your calculator to solve this system for 'a', which is the coefficient of the quadratic term.
- Once you have found the value of 'a', you can write the complete vertex form of the quadratic equation.
If you are given numerical values for the vertex and the point, you would substitute them into the equation as follows:
- For the vertex (h,k), your incomplete vertex form would be y = a(x - h)² + k.
- For the point (x, y), you would substitute these values in place of x and y in the equation, which allows you to solve for 'a'.
- For example, if the vertex is (3, -2) and the point is (4, 2), the system of equations to solve would look like: Through this, you would find that a = 4.
- The final vertex form of the equation would thus be y = 4(x - 3)² - 2.