**Determine the y-intercept, x-intercept, axis of symmetry, and vertex of y=(2x-3)(x+4). Please explain how to do it too!**

**Answer:**

y-intercept:

The y-intercept is where x=0, so substituting x in for 0:

y=(2(0)-3)(0+4)

= (-3)(4)

=-12.

x-intercepts:

The x-intercept is where y=0, so:

0=(2x-3)(x+4).

Since 0 multiplied by anything is 0, we can look at this as 0=2x-3 and 0=x+4.

0=x+4

x=-4 is an x-intercept.

0=2x-3

x=3/2 is the other x-intercept.

So the x-intercepts are -4 and 3/2.

Axis of Symmetry:

To find the Axis of Symmetry, use the formula x=-b/2a.

The equation needs to be in the quadratic form of y=ax^2 + bx +c to find a and b:

y=(2x-3)(x+4)

=2x^2 +8x -3x -12

y=2x^2+5x-12, so a=2 and b=5.

Using the formula for the Axis of Symmetry:

x= -5/(2)(2) = -5/4 as our Axis of Symmetry.

Vertex:

The x-coordinate of the Vertex is the Axis of Symmetry, which we found to be -5/4. To find the y-coordinate of the Vertex, substitute x=-5/4 into the original equation:

y=(2(-5/4)-3)((-5/4)+4)

= (-10/4 - 12/4)(-5/4 + 16/4)

= (-22/4)(11/4)

= 121/2.

The Vertex is (-5/4, 121/2).