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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.$$y=-4 x^{2}-5 x+12$$

$$\text { (b) }-2.5,1.2(\mathrm{c}) \frac{5 \pm \sqrt{217}}{8}$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

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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Okay, We're looking at this equation Y equals negative four X squared minus five X plus 12. And we are asked to graft this. So probably the easiest thing to mention is that you have a y intercept at 12 0 12 because if you plug in zeros, you have 090 plus 12. So it makes perfect sense that why intercepted the that? But then what you can do is find the access of cemetery by using the equation Negative B over two A. So we're looking at, uh, well, B is negative five. So it's a positive 5/2 times negative for so looking at negative because of possible Renee was negative. 58 So a little bit beyond the halfway point between zero negative one. You'll have a vertex that somewhere up here I don't know exactly where, um and a downward parabola and you might be sitting there and saying, Well, how do you know it's a downward parabola? Because the A value is negative. So our vertex is somewhere up here, But anyway, that's this is where our graph is located for part A, and you can use that graph for part B to estimate your X intercepts of about negative 2.5, you can use a graphing calculator. I think that's fine. Um, and 1.2, which I think it makes perfect sense that your negatives route your negative X intercepts a little bit further to the left. Then you're positive. X intercept barely passed one. Um, but then, in part C, you can find the X intercepts by using the quadratic formula. X equals negative B five plus or minus the square root of B squared minus four A. C. Okay, all over to a and, uh, yeah, you probably just need a calculator to figure out that under the radical square root of 217 that's all I did. Uh, and then you can divide everything by negative because the plus or minus isn't going to change when you divide by negative. But that's why we have a negative in front all over eight. Um, yeah, I think there's a perfect answer or your roots Mhm

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