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Question 4C0/10 ptsWite an equation (any form) for the quadratic graphed belowQuestion Help:Message instructorSubmit QuestionQuestlon 5G010 pts 56...

Question

Question 4C0/10 ptsWite an equation (any form) for the quadratic graphed belowQuestion Help:Message instructorSubmit QuestionQuestlon 5G010 pts 56

Question 4 C0/10 pts Wite an equation (any form) for the quadratic graphed below Question Help: Message instructor Submit Question Questlon 5 G010 pts 56



Answers

Write a quadratic equation having the given numbers as solutions. $-5,$ only solution

For a number 53 would've right the quadratic equation that this is the solution of. So I'm going to do it where it turns out to be zero. So I need to terms either, which makes this zero. So for this to be zero, I could have X plus five because X was negative five plus five. This would be zero. And over here I could have X plus six because negative six plus six would be zero. So now I just need to foil this. So I'm doing first. X Times X elder, So x time. Six. So six x dinner five times sex and last five times six is 30. And I could just combine these two inter terms here. So x squared plus 11 x plus 30 equals zero.

They would need through a function within steps. Months 3050 and 04 Let's get a graph on my mark on where these and Cepsa minus 30 50 on and Sarah four. And then the simplest choice would be a quadratic. Such that, uh, we have roots at minus three and five on the wind cept is for thank you.

We need to find the equation of the given quadratic. So we're first going to find our vertex, so our vertex is located at negative 12 Then we're going to use the Y intercept which is 03 So the vertex equation is alphabet X. Is equal to eight times the quantity x minus h squared plus K. So our H and K come from our vertex R X and F of X come from our Y intercept. So we have three is equal to eight times a quantity zero minus negative one squared plus. To this simplifies to be three is equal to eight times positive one squared plus two. We move our two over by subtracting, we get one is equal to a one A. We divide both sides by one and we get a. Is equal to one. So our equation is F of X is equal to one times a quantity X minus and negative one squared Plus two. Which cleans up to be the f of X is equal to the quantity X plus one squared plus two. So that's vertex form. So we're going to change it to general form. Mhm. So F of X is equal to foil, X square plus two X plus one plus two, which becomes F of X is equal to X square plus two X plus three.

We need to write an equation for the given quadratic. So we're first going to find our vertex sort of vertex is located at 11. Then we need another point on our vertex. So we have our y intercept which is 02. So we're going to use the vertex form of the equation which is F of X is equal to a times x minus h squared plus K. H. And k come from our vertex X and Y or X and f of X are going to come from our Y intercept. So we replace our values. So we have two is equal to a times zero minus one squared plus one. So we simplify this is negative one squared plus one. We move the one over so that's one is equal to one A. We divide both sides by one and we get A is equal to one. So the equation of our our quadratic function is F of X is equal to one times a quantity x minus one squared plus one, which simplifies to be the quantity x minus one squared plus one.


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