This week in precalc we learned how to analyze quadratic functions. We also learned how to use desmos to graph and see how parent functions transform. A quadratic function is written y = a + bx + c .

*Note the difference between equations and functions.*

Equations: you can solve and find roots.

Functions: you can graph, and find Y-intercepts and X-intercepts.

The parabola is the curve where any point is at an equal distance from. The vertex is the highest/lowest point, it may be a minimum or maximum point. The line of symmetry is the line that divides the parabola into mirror images.

When analyzing quadratic functions in a graph, we always need to look for the y-intercept, the x-intercept, the domain and range, parabola, vertex, line of symmetry, if it’s opening down or up, and if it’s congruent to the parent function.

How do we know how parent functions transform:

here’s the video and the link to the website that helped me understand how parent functions transform:

https://youtu.be/dJLQ8UOIuZ4  https://www.purplemath.com/modules/fcntrans.htm

On week 7 we learned a little about the discriminant, and the formula used is – 4ac . It helps determining how many solutions and real roots an equation has. The discriminant is pretty much the number you get under the square root in the quadratic formula.

If the answer to the equation is more than 0 there are 2 solutions, two distinctive real roots.

If the answer to the equation is equal to 0, then there is 1 solution (2 equal solutions), one real root.

If the answer to the equation is less than 0, there are no solutions, no real roots.

1.) 2 solutions

2.) 1 solution or 2 equal solutions

3.) no solutions