Question 3 (10 points) (08.07 HC) An expression is shown...

Question 3 (10 points) (08.07 HC) An expression is shown below: f(x) = 4x^2 + 8x - 5 Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points) Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

Transcript

00:01 So this problem is broken down into three parts.

00:02 I'm given a function, f of x equals 4x squared plus 8x minus 5.

00:06 And right off the bat, i can tell that this is a quadratic function because it has a degree 2.

00:12 So this is a quadratic function.

00:13 I'm asked to find in part a, what are the x intercepts? so in order to find the x intercepts, first of all, i'm going to need to factor this quadratic expression and set those factors equal to zero.

00:26 So multiplying a and c together, i get negative 20, and i need to find two numbers that multiply to make.

00:30 Negative 20 and add up to 8, which are going to be 10 and negative 2.

00:36 10 times negative 2 is negative 20, 10 plus negative 2 is 8.

00:39 I'm going to be using the method of factoring by grouping.

00:42 You might have learned a variety of different ways on how to factor.

00:45 I'm going to use the method of factoring by grouping.

00:47 So i'm going to rewrite this expression, 4x squared plus, and instead of 8x, i'm going to write plus 10x minus 2x, splitting up that term into these two numbers that i found, minus 5.

00:58 Then i'm going to proceed to factor by grouping.

01:01 So a greatest common factor in these first two terms, 4x squared and 10x, is 2 and x, leaving me with 2x plus 5.

01:08 A greatest common factor between these two terms, the only thing in common is they're both negative.

01:12 So if i take a greatest common factor of negative 1, i'm left with 2x plus 5.

01:17 So since i have a greatest common factor between the first and second half of this expression of 2x plus 5, that leaves me with 2x minus 1 .5.

01:30 2x plus 5 and 2x minus 1 are my two factors.

01:33 Now to find the x intercepts, i'm going to set both of those factors equal to 0, giving me x equals negative 5 halves and positive 1 half.

01:44 Those are my 2x intersets.

01:46 I'm going to go ahead and start drawing a graph so we can eventually see what this looks like.

01:53 So i have an x intercept right here at 1 half and right here at negative 5 halves, which is like negative 2...

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