what is the discriminant of the quadratic y= -3x^2 - 4x - 3
also explain what the graph will look like??
thanks
Discriminant is:
Ä=b^2-4*a*c
In this case:
a=-3
b=-4
c=-3
Ä=(-4)^2-4*(-3)*(-3)
=16-4*9
=16-36
=-20
Go to
en wikipedia and type "Discriminant"
Heare you have all about Discriminant
Also in google type
"wikipedia quadratic equation"
In this case when Discriminant is negative equation have two distinct complex roots.
To find the discriminant of a quadratic equation, you can use the formula: discriminant = b^2 - 4ac, where the quadratic equation is in the form ax^2 + bx + c = 0.
In your case, the quadratic equation is y = -3x^2 - 4x - 3. Comparing this equation to the standard quadratic form, we have a = -3, b = -4, and c = -3.
Now let's substitute these values into the discriminant formula:
discriminant = (-4)^2 - 4(-3)(-3)
discriminant = 16 - 36
discriminant = -20
The discriminant of the quadratic equation is -20.
Now, let's discuss what the graph of this quadratic equation will look like. Since the discriminant is negative, there are no real roots for this equation. This means that the graph will not intersect the x-axis.
Since the coefficient of x^2 is negative (-3), the graph will open downwards. This means that it will be a downward-facing parabola.
Also, since the coefficient of x^2 is greater than the coefficient of x (-4), the graph will be narrow or compressed.
The vertex of the parabola can be found by using the formula x = -b/2a. In this case, x = -(-4) / (2*-3) = 2/3. Substituting this value into the equation, we can find the y-coordinate of the vertex. y = -3(2/3)^2 - 4(2/3) - 3 = -1 - 8/3 - 3 = -16/3.
Therefore, the vertex of the graph is (2/3, -16/3).
Overall, the graph of the quadratic equation y = -3x^2 - 4x - 3 will be a narrow, downward-facing parabola that does not intersect the x-axis. The vertex of the graph is at (2/3, -16/3).