Quadratic Equations Help!?

Question

I am having trouble with my math homework, and i have the unit test tomorrow! Can someone pretty please explain in detail on how to solve this question? 1) Find in VERTEX FORM the equation if the quadratic relation with the vertex (-1, -4) and passing through the point (3, 4). If you could please tell me why you are doing certain steps im sure that would help a lot, because i have many more questions like this one. :) Thank you for helping!

Answer 1

Vertex form is in the form y = a((x - h)^ 2) + k, where (h,k) is the vertex of the equation. So with the points you described, we know that the equation is y = a((x + 1)^2) - 4 (h is +1 because two negatives equal a positive). To find the answer, substitute the point (3,4) into the equation:



4 = a((3 + 1)^2) - 4



4 = 16a - 4



8 = 16a



a = .5



The vertex form of the equation would be y = .5((x+1)^2)-4



EDIT: To convert to standard form, simply expand the equation



y = .5(x^2 + 2x +1) - 4



y = .5x^2 + x - 3.5 and there you have standard form.

Answer 2

One common term that looks commonly is "equations." for many, it quite is a buzz word it is recognizable as a math term yet fairly expertise the term would sometime get away human beings. the two commonest equations are linear equations and quadratic equations yet, needless to say, only giving an equation a popularity does not inevitably clarify what it is. So, a clearer definition of what precisely the two commonest equations - linear and quadratic equations - is important. A linear equation refers to a undeniable equation it is graphed on a right this moment line. additionally, a linear equation possesses on the line one variable it is frequently observed as "X" and "X" will continuously be of a level it quite is a million at maximum. (it is, there are not any exponents; yet once you're searching for exponents then wait and notice through fact we can get to them presently!) a common occasion of a linear equation could be 1x + 2 = 3. for sure, x could equivalent a million in this actual occasion and it quite is found out via only employing somewhat algebra on the equation to ensure X. 3 minus 2 equals a million. subsequently, X ought to equivalent one as a million x a million equals one. And, nope, no longer all linear equations are that hassle-free as they arrive as complicated as 6(x + 3) = 24 (x +0), however the common ingredient of keeping apart x to uncover the respond does not substitute. A quadratic equation is purely diverse from a linear equation in one know: various of of the figures is squared. (The word quadratic derives from the Latin word for squared) the common style of a quadratic equation is ax2 + bx + c = eleven. In the style of equation, if a = a million, b = 2 and c = 3 then X ought to equivalent 2. all of us be attentive to this through fact 2 squared is 4 and four x a million = 4. 2 x 2 = 4. As with a linear equation, there would be extra complicated variations of a quadratic equation yet purely with the hassle-free and complicated linear equations basic algebraic operations can yield the luxurious answer.

Answer 3

Hello,

Here is a good web site.

http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

Hope This Helps!