Question

how would i find the vertex,axis of symmetry, y and x intercepts, max/min value, range of 2x^2+5x-3?

Answer 1

Did we go over this earlier?

Answer 2

yep haha, but I'm preparing for a test this time.

Answer 3

people don't trust you rickjbr hahha :D

Answer 4

lol guess not

Answer 5

The vertex is at
\[(\frac{-b}{2a},f(\frac{-b}{2a}))\]

Answer 6

In this form, that is, ax^2+bx+c

Answer 7

The axis of symmetry is at the x-coordinate of the vertex, the max or min is at the y coordinate of the vertex

Answer 8

To find the y-intercepts, set x=0.
To find the x-intercepts, set y=0.

Answer 9

ax^2+bx+c
if a < 0, the y-coordinate of the vertex is a maximum because the parabola opens down.
if a>0, the y-coordinate of the vertex is a minimum because the parabola opens up.

Answer 10

You should try to find everything yourself. Others will review your work.

Answer 11

i understand most of the ideology behind this, but can your further explain how i get the vertex part

Answer 12

Tell me what a, b, and c are

Answer 13

ouchhhhhh :D

Answer 14

Have to start from the beginning, don't we?

Answer 15

a=2, b=5, c=-3

Answer 16

Right, so what is:
\[\frac{-b}{2a}\]

Answer 17

-5/4

Answer 18

good, that's the x-coordinate of the vertex.

Answer 19

how do we find the y-coordinate?

Answer 20

plug -5/4 into x?

Answer 21

that's right

Answer 22

so what'd you come up with?

Answer 23

sec pls haha

Answer 24

50/8-25/4-3?

Answer 25

no

Answer 26

how would you do it?

Answer 27

\[2(\frac{-5}{4})^2+5(\frac{-5}{4})-3\]

Answer 28

how would you simplify that then?

Answer 29

\[2(\frac{-5}{4})^2-\frac{25}{4}-3=2(\frac{25}{16})-\frac{25}{4}-3\]

Answer 30

\[=\frac{50}{16}-\frac{25}{4}-3\]

Answer 31

ohhhh

Answer 32

-50/16-3?

Answer 33

That's equivalent to the correct answer, but you can simplify it more

Answer 34

-98/16?

Answer 35

Keep going.

Answer 36

What is -98/16 simplified?

Answer 37

49/8

Answer 38

-49/8

Answer 39

my bad, but i get that.

Answer 40

So what's the vertex

Answer 41

(-5/4, -49/8)

Answer 42

good, what's the axis of symmetry?

Answer 43

-5/4

Answer 44

x=-5/4

Answer 45

Does this function have a maximum value or minimum value?

Answer 46

mi

Answer 47

n

Answer 48

how do you know?

Answer 49

2 is positive

Answer 50

right, so what is the minimum value

Answer 51

same as vertex

Answer 52

the minimum value is not a point

Answer 53

? how so

Answer 54

the minimum value is -49/8

Answer 55

ohhhh, min y value. ok ok

Answer 56

now, what's the range of this function?

Answer 57

(-infinity, -49/8]U[-49/8, infinity)

Answer 58

does this graph ever reach negative infinity?

Answer 59

nope

Answer 60

then what's the range?

Answer 61

i gave you the range though...?

Answer 62

but it's wrong

Answer 63

Hint: the function has a minimum value

Answer 64

both would be positive (-49/8, infinity)?

Answer 65

Is the vertex included in the range?

Answer 66

not sure. vertex the zero of the equation?

Answer 67

Is the minimum value included in the range, instead?

Answer 68

The function is defined at the minimum...
Range: [-49/8, infinity)

Answer 69

got it.

Answer 70

ok, what are the y-intercepts

Answer 71

what is the y-intercept***, there is only 1

Answer 72

3

Answer 73

not quite

Answer 74

-3?

Answer 75

right, x=0 at the y-intercept.
The y-intercept is then (0,-3)
Don't forget it is a point

Answer 76

What are the x-intercepts?

Answer 77

x-intercepts im not sure about.

Answer 78

OK, in this particular example, we can factor it. This isn't always the case, so you might need the quadratic formula

Answer 79

2x^2+5x-3
2x^2+6x-x-3
Can you factor from here?

Answer 80

This is the grouping method

Answer 81

unfamiliar with the grouping method. but x(2x+5)

Answer 82

Do you know the quadratic formula?

Answer 83

Any way you get the x-intercepts is fine, be it factoring or using the quadratic formula

Answer 84

Can you factor 2x^2+5x-3 without grouping?

Answer 85

(2x )(x )

Answer 86

sorry, got distracted.

Answer 87

so, can you get the x-intercepts?

Answer 88

trial and error is fine, this can be factored

Answer 89

lol. rickjbr, something came up i extremely appreciate your help. thanks for going through the steps with mua.

Answer 90

ill come back to this when i have the chance. But thanks you again.