please someone help with Quadratic equation y = -2x2 - x + 3!!?

Question

hello!! I really can use some help with this quadratic equation!! Its really hard and i dont understand how to do it!! than you soooo much!!

y = -2x2 - x + 3



What point is its vertex?
(-1/4, 25/8)
(2, 3)
(2/3, -2)
(-1/4, 4/9)


What is its axis-of-symmetry?
-1
2
2/3
-1/4


What are its x-intercepts?
{-2, 3/2}
{1, -3/2}
{-1, 3}
{4, -4}


What is its y-intercept?
3
-1/2
7
-2

Answer 1

note, given -2x^2 - x + 3
the vertex is at x = -b/(2a)
x = --1/(2(-2) = -1/4
when x = -1/4, then
y = -2[(-1/4)^2 - (-1/4) + 3
y = -2(1/16) + (1/4) + 3
y = -1/8 + 1/4 + 3 = 1/8 + 3 = 1/8 + 24/8 = 25/8
VERTEX
(-1/4, 25/8)

Axis of symmetry is at x = -b/(2a), and seeing above it is at
-1/4

x - intercepts are when -2x^2 - x + 3 = 0
which factors as
(2x + 3)(-x + 1) = 0
x = -3/2, 1
x = {1, -3/2}

y-intercept is when x = 0
so y = 3

Note: PHILO made a small mistake; use mine!

Answer 2

Axis of symmetry is x = -b/2a, so x = -1/4

The vertex lies on the axis of symmetry so plug x = -1/4 into y=-2x^2-x+3 getting y = -1/8 +1/4 + 3 =3 1/8 = 25/8. So vertex is (-1/4, 25/8).

x-intercepts are 1 and - 3/2 using quadratic formula.

Set x = 0 and get y = 3 ,so (0,3) is y-intercept.

Answer 3

y = -2x^2 - x + 3 = -(2x+3)(x-1)

Therefore, you can have all the answers immediately.

What point is its vertex? (-1/4, 25/8)
What is its axis-of-symmetry? x = -1/4
What are its x-intercepts?{1, -3/2}
What is its y-intercept? 3

Answer 4

Intercepts on x axis while y = 0 2*x^2 - 8*x + 6 = 0 2*(x^2 - 4*x + 3) = 0 2*(x - 3)*(x - a million) = 0 ie x - 3 =0 or x - a million = 0 subsequently x intercepts at x = a million or x = 3.<<< Intercept on y axis while x = 0 y = 2*x^2 - 8*x + 6 only set x = 0; then y = 6 Intercept on y axis while y = 6.<<<

Answer 5

y = -2x² - x + 3
y = -2[x² + (1/2)x] + 3
y = -2[x² + (1/2)x + 1/16] + 3 - 1/8
y = -2[x + 1/4]² + 23/8

so vertex is (-1/4, 23/8) and
axis of symmetry is x = -1/4

x intercepts when y = 0
0 = -2[x + 1/4]² + 23/8
(x + 1/4)² = 23/16
x + 1/4 = ±[√23] / 4
x = -1/4 ± [√23] / 4

y intercept when x = 0
y = -2(0)² - 0 + 3
y = 3

Answer 6

-2x2, is that -2 times 2 or is that another X?

use * for multiplication, it is less confusing.

try to combine any like terms...