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(a) Draw the graph of the parabola. (b) From your graph, estimate the $x$ -intercepts. (c) Check your estimate by finding the $x$ -intercepts exactly.$$y=-3 x^{2}+5 x-8$$

(b) None (c) None

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Campbell University

McMaster University

University of Michigan - Ann Arbor

Idaho State University

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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(a) Draw the graph of the …

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So we need a graph. This problem. Why Goals Negative three X squared plus five X minus eight. And the first thing to I guess point out, is that minus eight that see value is going to be your y intercept because if you plug in zero for X, you'll get a Y value of negative 80 plus zero minus eight is negative. Eight. Um, the next thing I would do is find the access of cemetery. Which is that negative? B over two, a formula. So the B values five. Some like that. Negative 5/2 times you're a value negative. Three. So we're looking at a negative, very negative positive. 56 So let's say this is X equals one. My access. The cemetery is just going to be shooting smaller than one. So to the right there, and then I can use my graphic calculator by plugging in 56 for both those exes and figure out what the Y value would be for that Vertex. Now, a quick answer is that it's less than one away, so I know it's going to be, uh, less than three away, and it's going to be a downwards parabola. So your vertex is going to be about right here. Um, I might be off just a little bit, but you can use a graphing calculator by plugging in 56 here and here to get those exact values. Um, so this is a good graph. I know it's not perfect. I didn't find the y coordinate of the Vertex, but, um, it's pretty clear from this that there is no X intercept because it's opening down and we have a negative Y intercepts. I know there's more math into it. Uh, they will never cross the X axis. Um, and you can confirm that that's correct by doing the quadratic formula quadratic formula, which says that X equals negative b lesser minus the square root of B squared. So that's 25 minus four times negative. Three times negative. Eight. Uh huh. All over to a and what we get in the denominator is what's 12 times eight, which is 96 25 1996. It's going to be a negative number. I don't know what that number is, but when you try to square root and negative, you get a non real solution in other words, no X intercept. So that's your answer for B and C no X intercept with this graph. The letter a.

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