Question

Graph the function f(x)=x^2-4x - 5 on the coordinate plane.

Answer 1

Answer:

(a) (-1, 0) and (5, 0)

(b) (0, -5)

(c) (2, -9)

Step-by-step explanation:

f(x) = x² - 4x - 5  

(1) Create a table containing a few values of x and y

x   y  

-1     0

0   -5

1    -8

2    -9

3    -8

4    -5

5     0

(2) Plot your points

Draw markers (dots?) at the coordinates of each point.

(3) Draw the graph

Draw a smooth line through the points.

Extend the line in both directions to the edges of the plot area.

Your graph should look like the figure below.

(a) x-Intercepts

The x-intercepts are at (-1, 0) and (5, 0).

(b) y-Intercept

The y-intercept is at (0, -5).

(c) Minimum

The minimum is at (2, -9).

Answer 2

To factor it is (x-5)(x+1)

A) zeros ( also known as x-intercepts) are (5,0) and (-1,0)
How: x - 5 = 0. And x + 1 = 0
+5. +5. -1. -1
x = 5. And. x = -1

B) y- intercept. (0, -5)
Y= x^2 - 4x -5
0^2 -4(0) -5
Y = -5

C) since the x^2 term is positive, the parabola opens up and the graph has a minimum.
The minimum horizontally halfway between the zeros : (5 + -1)/2 = 2 ..... (2, )