Given:
Expand (x-2)^2.
y=2(x^2-4x+4)-3x
Simplify.
y=2x^2-8x+8-3x
Simplify.
y=2x^2-11x+8 is a quadratic equation in standard form:
y=ax^2+bx+c,
where:
a=2, b=-11, c=8
Vertex: the maximum or minimum point of a parabola
The x-coordinate of the vertex can be calculated using the formula for the axis of symmetry:
x=(-b)/(2a)
x=(-(-11))/(2*2)
x=11/4 or 2.75
The y-coordinate is determined by substituting 11/4 for x in the equation and solving for y.
y=2(11/4)^2-11(11/4)+8
Simplify.
y=2(121/16)-121/4+8
Simplify.
y=242/16-121/4+8
Simplify 242/16 to 121/8.
y=121/8-121/4+8
The least common denominator is 8. Multiply 121/4 by 2/2 and multiply 8 by 8/8 in order to get equivalent fractions with 8 as the denominator. Since n/n=1, the numbers will change but the value will remain the same.
y=121/8-(121/4xx2/2)+(8xx8/8)
Simplify.
y=121/8-242/8+64/8
Simplify.
y=(121-242+64)/8
y=-57/8 or (-7.125)
The vertex is (11/4,-57/8) or (2.75,-7.125).
graph{y=2(x^2-4x+4)-3x [-9.58, 10.42, -10.44, -0.44]}
