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Worked examples: Forms & features of quadratic functions

Choosing whether factored form, vertex form or standard form of a quadratic is best in different situations.

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• In my opinion, it's way easier to find the vertex with the standard equation by dividing negative of the coefficient of x with twice of the first coefficient or (-b/2a)
• Yeah I agree! I used that formula on my math test!
• /
Ok so I am very confused here. How exactly does Sal decide that Standard form is the best way to find y, because I thought that factored form was better at finding the Y?
• Notice, the examples in the video are asking Sal to pick the best form to find different information about the quadratic equation.

Standard form reveals the y-intercept. It is the constant term.

Factored form is best for finding the x-intercepts.

Vertex form is best for finding the vertex of the parabola.

Hope this helps.
• Why the zeros of a function is called the roots of a function?
What is the meaning of root in the context of the zeros of a function?
Thanks
• The factored form returns the roots (x-intercepts) of a function, because you got a polynomial expression and try to separate and solve it into factors - either by guessing, quadratic formula or polynomial division.
• At about minutes into the video, Sal said; "this is 'always' going to take away from the 18."
There is one scenario where it won't, and that is when x = 6 right?
Why did he say this then?
• Technically, you can still take away 0 from 18, since 18-0=18, it's just that nothing happens.
• Why and how does m(x)=y?
• When you write equations, you can write them in function notation, for example m(x)=5x^2. You can also write that as y=5x^2
• How do you evaluate -3x^2+36x+33 to find its vertex?
I end up at x^2-12x-11 which has no factors, if not mistaken.

When I tried using the Quadratic Formula, I ended up with 6 +/-√188 <- is this correct? I don't know how to further simplify this given that 188 has no actual square root.
• The height (h) in feet of a ball (t) seconds after being tossed upwardis given by the function h(t)=56t-8t squared
• How do you REALLY know which one of the equations/expressions are vertex, factored, or standard form?
• The three forms use letters instead of numbers,
So standard is f(x) = ax^2+bx+c so no parentheses
Factored form is g(x) = (ax+b)(cx+d) so they look like factors that could be solved using the zero product rule
Vertex form uses different letters h(x)=a(x-h)^2+k, and for other functions as well as the quadratic, the vertex is at (h,k).