Quadratic equations
Quadratic equations.
When a quadratic equation given in the form 〖ax〗^2+bx+c=0 or (x+p)(x+q)=0 , these parameters a, b, c, p and q are related to the graph. With this activity you will undestand the relation of most of those parameters to the graph. You will be able to know the solution of an equation just by looking at the graph. You will alsot know the y-intercept and the shape of the parabola you have to draw just by looking at the equation.
1. On top of the screen on the right side, there are some sliders (horizontal bars). Slide p and q. Try at least 8 different values for each variable and observe what happens with the equation on the left in each case.
1.a. Describe the relation you have observed between the values of p and q in the equation and the graph.
1.b. Explain how you could know the solution of a quadratic equation just by looking at the graph.
2. Move c on the sliding bar.
2.1. Try at least 8 different values for c on the right and observe what happens. Describe the relation between c in your equation and the graph.
2. 2. Explain how you could know the y-intercept of a quadratic equation just by looking at the equation.
3. Click on the function g(x) and change the sign in front of x^2. Try different values with different signs for a at least 6 times and describe the relation you have observed between the sign and the shape of the parabola.