Given y= 2x squared-3x+1?

Question

Determine each of the following a,b,c
the y-intercept(state the formula then the answer)
the x-intercept(state the formula then the answer)
the axis of symmetry (state the formula then the answer)
the vertex(state the formula then the answer)

Answer 1

a=2, b=-3 , c = 1

y-intercept occurs when x=0
y=1, intercept at (0,1)

x-intercept occurs when y=0
0= 2x^2 - 3x + 1
factorise this, (2x-1)(x-1)=0
either 2x-1 = 0 or x -1 = 0
x = 1/2 or x = 1
intercepts at 1/2,0 and 1,0

axis of symmetry x = -b/2a
=--3/2x2
=3/4
x= 0.75

vertex occurs when x = 0.75
y = 2x0.75^2 - 3x0.75 + 1
y = - 0.125
vertex at (0.75, -0.125)

Answer 2

Substitution skill you're taking between the variables in a single equation and replace it in the different. Or, y = 3x + 2 in a single equation, so which you would be able to easily plug the 3x + 2 into the different equation to unravel for x: 2x + y = 5 is going to 2x + (3x + 2) = 5 2x + 3x + 2 = 5x + 2 = 5 resolve for x: 5x = 5 - 2 = 3 x = 3/5 then you certainly can positioned the value you discovered for x into the two equation to discover y: y = 3x + 2 is going to y = 3 (3/5) + 2. y = 9/5 + 2 y = 9/5 + 10/5 y = 19/5 so... x = 3/5 and y = 19/5

Answer 3

1

Answer 4

y= 2x squared-3x+1
The y-intercept occurs when x = 0, so f(0)= 1. Therefore the y intercept is (0,1).

The x-intercepts are x = [-b +/- sqrt(b^2-4ac)]/(2a)
The x intercepts occurs when y =0. Since y= (2x-1)(x-1), then y will be zero if x = 1/2 or x = 1. Thus the x-intercepts are (1/2,0) and (1,0).

x = -b/2a
x = 3/(2*2) = 3/4 is the axis of symmetry.

The vertex lies on the axis of symmetry so its y value is
f(-b/2a) = f(3/4) = 2(3/4)^2 -3(3/4) +1 = -1/8
So vertex is at (3/4,-1/8). Since a> 0, this is the minimum value of the parabola.

Answer 5

y(x) = 2x^2 - 3x + 1 = (2x-1)(x-1)
If y= 0 then x = 1/2, 1 the x-intercepts
If x = 0 then y = 1 the y-intercept
y'(x) = 4x - 3 =set=0
x = 3/4 an extremum, the vertex

Answer 6

i can only answer the first three sorry.


y intercept is when x = 0

hence, y = 1

x intercept is when y = 0
2x^2-3x+1=0
(2x -1)
(x-1)
(2x-1)(x-1)=0
x = 1/2 or x = 1

axis of symmetry = -b/2a
3/2(2)
x=3/4