Help with math, the quadratic formula?

Im not asking you to do it but help me get a better explanation, i wasnt at school for a week because my grandpa was in the hospital, i am in the 9th grade..





It is asking my to use the quadratic formula to find the soltions of the wquation,





0=xsquared-5x+3





squared means exponet 2 so x2 but a exponent.





Its asking me to find the





x=


x=





help?





And also i am asked to expand the poducts





c(c-7)








(x - 3)(x + 5)





-2x(x + 12)








and to find the x-intercepts and the y-intercepts of the graph function. and asked to factore it.





y=xsquared-5x





theese are a couple examples of the hundreds of problems i have to do for makup.. Please help, thank you.





My math teacher is a penis, so he told me to go to the tutor during lunch but i had a lab bio test to makeup.





Thank you

Help with math, the quadratic formula?
Hi there Joseph. I'm sorry to hear about your grandpa - hope he's okay.





Your topic is binomial products - I'll go through it for you. Sorry if some of this is basic to start with...





Consider 2(a + b) = (a + b) + (a + b) = 2a + 2b


In other words: 2(a + b) = 2 x a + 2 x b = 2a + 2b


Everything inside the brackets is multiplied by the term outside of the brackets.





So a(a + b) = a x a + a x b = a² + ab





Then, c(c - 7) = c x c - c x 7 = c² - 7c


Also, -2x(x + 12) = -2x x x + -2x x 12 = -2x² - 24x





The next part of your work, (x - 3)(x + 5) involves multiplying everything inside each bracket by each other





A system of doing this is FOIL, where


F = First terms


O = Outer terms


I = Inner terms


L = Last terms.





In the question (x - 3)(x + 5),


* the first terms are x and x


* the outer terms are x and 5


* the inner terms are -3 and x


* the last terms are -3 and 5





Using FOIL, we get


F: x times x = x²


O: x times 5 = 5x


I: -3 times x = -3x


L = -3 x 5 = -15


As working, we write


(x - 3)(x + 5) = x² + 5x - 3x - 15 = x² + 2x - 15





The quadratic formula is a method of going backwards through a question (to get back to brackets) and find the solution. It's a big formula:





x = [-b ± √(b² - 4ac)] ÷ (2a)





The letters a, b and c come from the 3 parts of the quadratic expansion. In your case:


0 = x² - 5x + 3


a = 1 (from the first term, 1x²)


b = -5 (from the second term, -5)


c = 3 (from the third term 3)





Putting this into the formula:





x = [-b ± √(b² - 4ac)] ÷ (2a)


x = [-(-5) ± √(-5² - 4 x 1 x 3)] ÷ (2 x 1)


x = [5 ±√(25 - 12)] ÷ 2


x = [5 ±√13] ÷ 2





± means plus / minus (it gives you two possible answers).





So the two answers for your question are:


x = [5 + √13] ÷ 2 (≈ 4.3)


x = [5 - √13] ÷ 2 (≈ 0.7)





For your final question, y = x² - 5x


Factoring means taking out common factors:


y = x² - 5x becomes y = x(x - 5)


The x intercepts happen when y = 0.


0 = x(x - 5)


When x = 0 or x = 5, y = 0





The y intercept happens when x = 0


y = 0(0 - 5) = 0


So the y intercept is at y = 0





Trust all this helps...there's much to know and learn.