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

y2x-3x4

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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).