Tell whether each of the following parabolas opens upward or downward?

Question

a. y=x^2-1
b. y=-3x^2

Thanks.

Also, If anyone knows how to do this..please help me.

Solve using the quadratic formula.
5x^2-3x-3=0

THANKS!! MERRRRRY XMAS!

Answer 1

Question a.
Upwards
Can test by using a few points:-
(- 1 , 0), (0, - 1) , (1 , 0)
Vertex (0 , -1)

Question b.
Downwards.
A few points:-
(- 1 , - 3) , (0 , 0) , (1 , - 3)
Vertex (0 , 0)

Question c.
x = [ 3 ± √(9+ 60) ] / 10
x = [ 3 ± √(69) ] / 10

Have a good day!

Answer 2

a.) the parabola opens upward. any value for x squared is positive and quickly exceeds 1 so the value of y will be positive.

b.) the Parabola opens downward. any value for x squared is positive. That value times -3 will becomes a negative value therefore Y will always be negative.

for equations of the general form Ax^2 + Bx +C
the signs may be plus or minus the formula works.
The quadratic formula is:
x= -B+- sq rt B^2-4AC/2A
in your case 5x^2-3x-3=0
A=5 B= -3 C= -3

x= -(-3) +- sq rt -3^2- 4x5x -3 /2x5
x= 3 +- sq rt 9 + 60 /10
x = 3 +- sq rt 69 /10
x = 3 +- (8.3) /10
x = 11.3/10= 1.13 or -5.3/10 = -.53

see the link below for a full explanation of the quadratic formula

Answer 3

A parabola opens upwards if the coefficient of the x² is positive.

Therefore a) opens up, and b) opens down

The quadratic formula is:

x = [-b ± √(b^2 - 4(a)(c))] / 2a

Where a = 5, b = -3, and c = -3 in your case.

x = [3 ± √((-3)^2 - 4(5)(-3))] / 2(5)

x = [3 ± √69] / 10

x = approx. 1.130662386 or x = approx. -0.530662386

Merry Christmas :)

Answer 4

think about the behavior of the parabola as x goes to plus and minus infinity, you know that the x^2 will dominate, so the behavior of the parabola at large values of x will be determined by the behavior of x^2.

if the coefficient of x^2 is positive, then the y value of the parabola is large and positive as you go to plus and minus infinity, which means the parabola must be pointing up (the minimum is somewhere between the endpoints)

if the coefficient of x^2 is negative, then the y value of the parabola is large and negative as x goes to plus and minus infinity, which means the parabola is pointing down (since the maximum value is somewhere between the endpoints)

so, x^2-1 point up
-3x^2 points down
5x^2-3x-3 points up

Answer 5

a. up
b. down

-(-3) + or - sqrt -3^2 - 4(5)(-3) over 10