Question

Describe the differences between the graph of y = –3(x + 7)2 – 10 and the standard position graph of y = x2.

Answer 1

please indicate whether its a 2 or a squared "(x+7)2"

Answer 2

yes it is squared

Answer 3

The parabola could be written as \(y = a(b(x-h)^2 + k\)
Where, a,b,h,k are some constants.

Answer 4

a describes the vertical stretch;
b describes the horizontal stretch;
(h,k) is the vertex.

Answer 5

In your parabole, can you identify a,b,h and k for me? :)

Answer 6

parabola*

Answer 7

y = –3(x + 7)^2 – 10
y=-3(x^2+49)-10
y=-3x^2-147-10
y=-3x^2-157

since the 3 is negative it indicate that the graph opens downward

*NOTE* if the number before the x^2 is negative the graph opens downwards, if it is positive then it opens upwards

the graph y=x^2
isnt this just y=1x^2
1 is positive so the parabola opens upwards INSTEAD of downwards.

Answer 8

@Brent0423 (x+7)^2 doesn't give x^2 + 49, it gives x^2 + 14x + 49.

Answer 9

As \((a+b)^2\ = a^2 + 2ab+b^2\)

Answer 10

oops thought i put that, sorry

Answer 11

you can still see the difference in the graphs just by looking at the number in front of the x^2

Answer 12

Let me find a,b,h,k for you :)
y = –3(x + 7)^2 – 10

-> y = –3(x - (-7))^2 – 10 (Notice the negative!)

-3 would be a, the vertical stretch
1 would be b, since there's nothing in front of x
Vertex would be at (-7, -10)

Now let's take a look at our basic parabola, y = x^2
a = 1
b = 1
Vertex: (0,0)

Since our a constant is a negative number AND greater than 1, we can say that this function has been stretch vertically of factor 3.
Then b is the same.
Vertex (0,0) and (-7,-10)

We can say that the parabola is moved of 7 to the left and 10 downward.