Arrange the parabolas represented by the equations in increasing order with respect to the y-values of their directrixes.
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y = -x2 + 3x + 8
y = 2x2 + 15x + 18
y = x2 + 13x + 5
y = -2x2 + 4x + 8

3rd Parabola < 2nd parabola < 4th parabola < 1st parabola.

Step-by-step explanation:

We are given with equation of parabolas.

We need to arrange them in increasing order with respect to y-values of their directrixes.

First we convert given equations in Standard form then find their directrix.

The standard form is (x - h)² = 4a (y - k),

then directrix is  y = k - a

1). y = -x² + 3x + 8

using completing the square method,

Now, by comparing with standard equation

So, Directrix,

2). y = 2x² + 15x + 18

using completing the square method,

Now, by comparing with standard equation

So, Directrix,

3). y = x² + 13x + 5

using completing the square method,

Now, by comparing with standard equation

So, Directrix,

4). y = -2x² + 4x + 8

using completing the square method,

Now, by comparing with standard equation

So, Directrix,

So, from above

y = 37.5 < y = -10.25 < y = 10.125 < y = 10.5

Therefore, 3rd Parabola < 2nd parabola < 4th parabola < 1st parabola.

step-by-step explanation:

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a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.