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Determine the equation of the parabola passing through the points (0,8)(2,6) and (-1,0)

$$y=-3 x^{2}+5 x+8$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Missouri State University

Oregon State University

Harvey Mudd College

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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So we need a proble That goes to the 0.8 26 and negative 10 Uh, So what I would use is, uh is this general form a expert plus BX plus C and I would use this point because of x zero zero times. Anything is still zero. Uh, basically what it boils down to C is equal to 80 plus zero plus secrecy. April's eight. So I'm gonna circle that. That's part of my answer. Um, So now what I can do is I can I would actually do this point next. Because of my zero, we'll think about when x is negative. One squared is positive. One when x is negative one times b plus my see value. So all I would do is subtract eight over uh, And then what I would probably do is use this point third and using that when y is six. X s two with two square this four star looking at four a plus to be an n plus eight. But again, I need to subtract 8/6 months. Eight is negative. Two equals four a plus to beat what I would probably do next is Multiply this equation by two so I can match up my bees again. Negative 16 equals to a, uh, minus to be so I can eliminate my booze. This is a You can use substitution if you wanted to. But now, as I add these two things together and make two plus nine of 16 to 18 for a plus 2 +86 a, those eliminate. And after I divide both sides by six, I get a equals negative three and that quick way to figure out what B is just to go back to this equation. So you have negative eight equals negative three minus B. So if I add three over, it's probably faster by. And I guess I was just divide both sides by negative one to get vehicles. Five. Uh, so having done all of that, I can go back to my original equation this thing and replace a with negative three. So why was negative three X squared B with five. I guess you forgot to search that. Underline that, and I see value was eight and those are my lips mess that up because this should be five X. There we go. That's correct. Super

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