Determine the y-intercept, x-intercept, axis of symmetry, and vertex of y=(2x-3)(x+4). Please explain how to do it too!
The y-intercept is where x=0, so substituting x in for 0:
The x-intercept is where y=0, so:
Since 0 multiplied by anything is 0, we can look at this as 0=2x-3 and 0=x+4.
x=-4 is an x-intercept.
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:
=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.
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:
= (-10/4 - 12/4)(-5/4 + 16/4)
The Vertex is (-5/4, 121/2).