Question

help with this pick one of the 3 equations at the top then answer the questions about the one you pick giving 98 points

Answer 1

The equation I picked was x^2+5x-6=3

1. the parabola opens up as the leading coefficient is a positive.

2. to find the vertex to find the x value
-5/2(1)= -5/2 (-2 1/2) (-2.5)
to find the y value of the vertex substitie the x value into the equation
(-2 1/2)^2+5(-2 1/2)-6=3
6 1/4 - 12 1/2 -9 = y
-15 1/4 = y
y = -15 1/4 (-15.25)

(-2.5, 15.25) , (-2 1/2, -15 1/4)

3. the y intercept can be found by substituting the X's with 0's
x^2+5x-6=3
first move the terms to the left
x^2+5x-9=y
(0)^2+5(0)-9=y
0+9=y
9=y
y=9

the y intercept is 9 (0,9)

4. b^2-4ac
5^2-4(1)(-9)
=25+36
=61
61 is greater than 0 so this means there are 2 real solutions.

5.
$x = \frac{ - 5 + - \sqrt{5^{2} - 4(1)( - 9) } }{2(1)}$
$x - = \frac{ - 5 + - \sqrt{61} }{2}$
$x = \frac{ - 5 + \sqrt{61} }{2} \: or \: x = \frac{ - 5 + \sqrt{61} }{2}$
the +- next to each other is meant to be plus or minus

6. to find three other points pick any x value and substitute that into the equation

y=(2)^2+5(2)-9
y=4+10-9
y=5

(2,5)

y=(3)^2+5(3)-9
y=9+15-9
y=15

(3,15)

y=(4)^2+5(4)-9
y=16+20-9
y=27

(4,27)

I hope this helps, brainliest?

Answer 2

Answer:

x^2+5x-6=3

1. the parabola opens up as the leading coefficient is a positive.

2. to find the vertex to find the x value

-5/2(1)= -5/2 (-2 1/2) (-2.5)

to find the y value of the vertex substitie the x value into the equation

(-2 1/2)^2+5(-2 1/2)-6=3

6 1/4 - 12 1/2 -9 = y

-15 1/4 = y

y = -15 1/4 (-15.25)

(-2.5, 15.25) , (-2 1/2, -15 1/4)

3. the y intercept can be found by substituting the X's with 0's

x^2+5x-6=3

first move the terms to the left

x^2+5x-9=y

(0)^2+5(0)-9=y

0+9=y

9=y

y=9

the y intercept is 9 (0,9)

4. b^2-4ac

5^2-4(1)(-9)

=25+36

=61

61 is greater than 0 so this means there are 2 real solutions.

the +- next to each other is meant to be plus or minus

6. to find three other points pick any x value and substitute that into the equation

y=(2)^2+5(2)-9

y=4+10-9

y=5

(2,5)

y=(3)^2+5(3)-9

y=9+15-9

y=15

(3,15)

y=(4)^2+5(4)-9

y=16+20-9

y=27

(4,27)