Week 9- Analyzing general form of quadratic equation

In week 9 of pre-cal 11 We learned how to analyze the general form of quadratic equation along with many things.

With analyzing, I mean you factor the equation if it’s factorable. And apply the knowledge I learned from last unit to find the two or 1 roots, and using logical thinking such as the axis of symmetry must have the same distance on the x axis to both roots and etc to find more information without changing the equation into standard form.

Week 8 – Graphing Quadratic Equations

In week 8 of pre-cal 11, we learned how to graph quadratic equations with the general form and the standard form.

a$x^2$+bx+c, is the general form of the equation, with this form the equation we can find limited information comes to graphing; we can determine the direction and the compression ratio of the graph from a, and y-intercept from c.

But we can easily change this equation to standard form by completing the square; $y=a(x-p)^2+q$ from this form of the equation we can determine the position of the vertex with q being the y-axis(+ going up,- going down), p being the x-axis(- going right, +going left) and the direction of opening and the compression ratio of the graph by looking at a,( the ratio of the graph will be congruent to a$x^2$=y, a determines the direction of the graph( if negative a, facing down, if postive a opens up).

Week7- Discriminants

During week 7 of pre-cal 11, we learned how to find the discriminant of a general form of a quadratic equation.

$x = \frac {-b +/- \sqrt {b^2 - 4ac}}{2a}$

The discriminant is the part under the root sign:

$b^2 - 4ac$

Finding the solution to the discriminant of a quadratic equation will provide you will the type of roots you will get from the aforementioned quadratic equation.

To find the discriminant of a quadratic equation you need to learn the meaning of a,b,c in this case:

a$x^2$+bx+c, is the general form of the equation, and when you are trying to find the discriminant just put $b^2$-4ac in, such as:

4$x^2$+2x+6, the discriminant will be $2^2$-4(4×6)=-92

And the range the discriminant is in it will provide you with the number of roots you will get from this quadratic equation; If your answer is a positive number, there are 2 roots, If your answer is a negative number, there are no real roots, If your answer is a 0, there is 1 root.