Without graphing, tell how many x-intercepts y=2xsquared +4x+2. explain?

Answer 1

2 because this is a quadratic equation and all quadratic equations have 2 roots. Here is proof
y=2x^2+4x+2
so
y=2(x^2+2x+1)
y=2(x^2+x+x+1)
y=2(x(x+1) + 1(x+1))
y=2(x+1)^2

when y = 0 we have that
0 = 2(x+1)^2

x1=-1 and x2=-1

thus 2 roots.

Answer 2

there would be 2, if you equate the function to 0, you would end up with 2 roots, which becomes the x intercepts if u equate them to zero, the reason why we change "y" into 0 is to ask that if y=0, where would x be? so in order to find the x intercept, we would equate the function(equation) to 0 in order to get the intercept, sometimes not all functions are factorable, and we have to use the quadratic formula, but simply to find all the available zeros of a function (zeros also mean x intercepts), we can use Descarte's Rule of Signs in order to find the zeros.....and presumably, in this equation there are no positive zeros (or no positive x intercepts) but instead there are 2 or 0 negative zeros....if you haven't learn precal yet, take it so you would understand what I'm trying to say

Answer 3

y=0

Answer 4

1 interception
It touches a one point of the X axis which is (-1,0)
therefore x =-1
Explanation

y=2x^2+4x+2
Since y becomes o when it touches the x axis
2(x^2+2x+1)=0
x^2+2x+1=0
(x+1)^2=0

(x+1)(x+1)=0 when this occurs it means its a complete square which gives u a repeated root
X=-1
Since both answers are -1 the it touches(not cuts) the x axis at( -1,0)
When u obtain a repeated root it means that the graph does touch that particular point which is the minimum point of the given equation.
So answer is -1

Answer 5

Like the above poster said, to find the number of roots of a quadratic equation (highest power of x is 2), you test the discriminant: b^2-4ac where the function is in the form y=ax^2+bx+c. In your case this is 4^2-4(2)(2)=16-16=0.
If discriminant is negative, no roots. Positive discriminant means two roots. Discriminant of 0 means one root. So you have one root. The whole discriminant thign is derived from the quadratic equation.

Answer 6

if you're asking how many times this graph intersects the x-axis then all you have to do is plug in y=0 and solve for x.

0=2x^2+4x+2

now use the quadratic equation and see how many solutions you get. It'll either be 2,1, or 0.

Answer 7

y=x^2+4x+2
has the form y=ax^2+bx+c
find the determinent
b^2-4ac
4^2-4*1*2=16-8=8>0 therefore there are 2 real roots, the curve crosses the x axis twice.

Answer 8

1 repeated root.

The discriminant (b² - 4ac = 4² - 4(4)(1)) is zero.

When this happens, it means that the equation is a perfect square, and there's a repeated root.

y = 2(x² + 2x + 1) = 2(x + 1)²

So there's a repeated root of x = -1.

The discriminant is the key.

b² - 4ac > 0 means 2 real roots.
b² - 4ac = 0 means 1 (repeated) root.
b² - 4ac < 0 means no real roots (or 2 complex conjugate roots).

Answer 9

because the higher degree of x is 2 or it's a quadratic function, so it will be intercept twice by x.
another just find the factors or zeroes from the polynomial, when you get the real number you get where the x got intercept.
check this..

Answer 10

There is going to be one x-intercept and all you do is factoring to solve it:

2(x^2+2x+1)=0
x^2+2x+1=0
(x+1)(x+1)=0
x=-1