What is quadratic of 4x2 3x - 6?

Answer 1

4x2 + 3x - 6 is a quadratic polynomial. Any polynomial determine a polynomial function.

Thus, f(x) = 4x2 + 3x - 6, which graph is a parabola that opens upward (4 > 0).

For any value of x, we can find a corresponding value of y.

If x = 0, then y = -6; (0, -6) the y-intercept point, which tells us that the parabola cuts the x-axis.

Let's find the values of x (the x-intercepts), which make f(x) = 0.

0 = 4x2 + 3x - 6 factor it since 4(-6) = -24 = 8(-3) and 8 - 3 = 5

0 = [(4x + 8)/4](4x - 3)

0 = (x + 2)(4x - 3) let each factor equal to zero

(x + 2) = 0 or (4x - 3) = 0 solve for x

x = -2 or x = 3/4 the x-intercepts

The axis of symmetry, x = -b/2a = -3/2*4 = -3/8. Thus, (0, -6) is symmetrical to (2*-3/8, -6) = (-3/4, -6).

Since the vertex lies on the axis of symmetry, the vertex is [-3/8, f(-3/8)].

f(-3/8) = 4(-3/8)2 + 3(-3/8) - 6 = 9/16 - 9/8 - 6 = (9 - 18 - 96)/8 = -105/8 = -(13 and 1/8) .

Thus, the vertex is (-3/8, -105/8).

Just plot the points and draw the parabola that passes through them.