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In Exercises 57 and 58, determine the x-intercept(s) of the graph visually. Then find the x-intercept(s) algebraically to confirm your results.

$ y = 2x^2 + 5x - 3 $

$\left(\frac{1}{2}, 0\right),(-3,0)$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

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Let's determine the X intercept visually from the grass and then we'LL go ahead and find the ex intercepts algebraic Lee to confirm our our guest from the graph. Now let's go on to the graph. Here we have our parabola. We could zoom in tow, find the exact values here. But let's not do that right now because we will find them. Lt break anyways. But based on the graph, it looks like if this is too, that this is is one, then this looks to be about a half, whereas the other one looks like about negative three. So for right now we're guessing. So that's based on the visual guests. And now let's go Algebraic leads to confirm. So in this case, the X and reserves are the while the values that give you equal zero. So we want to go ahead and set. This is quadratic equals to zero and then solve for X. While there are many ways to do this, one way to do this is to complete the square. Another methods to use the quadratic formula here. So if you have, then we know that we can go ahead and say the following by the contract IQ formula. Now, in our case, we have a sze to B is five c is minus three. So plugging these in into the contract IQ formula so have five squared minus four times two times of minus three and this is all over two times a day. So notice inside the radical. Here you have twenty five much out here for the double minus that turns into a plus. And then we'LL have eight times three, which is twenty four and giving this asshole of forty nine and we know the square root of that is seven. So all over four and then now I have to be simplified. So if you do the plus sign you get negative five plus seven, which is two. Divide that by four. That gives you a half. And if you do the minus sign, you have negative twelve over four, which is minus three. And these values do agree with our guests from the graph. So finally, we should go ahead and just write out these answers. Technically, the X intercept is on a number. It's a point. So we should right one half comma zero and then negative three comma zero. And these are answers

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