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In $9-14 :$ a Sketch the graph of each function. b. From the graph, estimate the roots of the function to the nearest tenth. c. Find the exact irrational roots in simplest radical form.$$\mathrm{f}(x)=x^{2}-6 x+4$$

a) graphb) The roots of $f$ rounded to the nearest tenth are the $x=0.8$ and $x=5.2$ as shown in the pic.c) $x=3+\sqrt{5}$ and $x=3-\sqrt{5}$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 1

Real Roots of a Quadratic Equation

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

McMaster University

Harvey Mudd College

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

05:45

In $9-14 :$ a Sketch the g…

03:58

08:40

04:00

06:25

00:46

In $9-14$ : a. For each gi…

00:39

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01:40

Okay, This question asks us about this quadratic function so first and wants us to graph the quadratic and estimate its roots to the nearest tent. So I went ahead and drafted in Dismas here. So this is our function after vax, and we want to know where f of X is equal to zero. So let's just where it crosses the X axis. So we see two points one here on one here and we see that are approximate X values free to these routes is for the first route. That's around 0.8 and the other route is around 5.2. So that's our estimates for the solutions. But we can actually find the solution exactly by completing the square. So we start with X squared minus six. X plus four equals zero, and we want to solve this. So we're going to complete the square by turning X squared plus B X plus c into are complete the square for him. Where d is equal to be over to a and E is equal to see minus B squared over four a. So let's find D and E S. O. D. Is equal to be over to a which is negative. Six over to or just negative three on then E is equal to C minus. B squared over four A, which is four minus. B squared is 36 divided by four A just four. So we have four minus nine, which is negative. Five. So that means we can transform our equation into X minus three squared minus five equals zero. So if we want to solve this equation now, this is something that's much more doable for us. I'm sorry. Minus five equals zero. So we just acted five. We just add five to both sides here and get X minus three is equal to five X minus two squared. So then we just take a square root and get X minus. Three is equal to plus or minus the square of five. So that means we have two options. We have X minus three equals positive square 25 and X minus three equals negative squirt of five. So we have X equals three plus Route five, and we have X equals three in minus root five as our solutions. And if we punch these into our calculator, we'll see that these are

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