Answer:
D. The axis of symmetry is x = 1.5 and the vertex is (1.5, 0).
Step-by-step explanation:
y=4x^2-12x+9:\quad \mathrm{Parabola\:with\:vertex\:at}\:\left(h,\:k\right)=\left(\frac{3}{2},\:0\right),\:\mathrm{and\:focal\:length}\:|p|=\frac{1}{16}
To find the vertex of this parabola, "complete the square:" Rewrite y = 4x2 - 12x + 9 in the form y = 4(x - h)^2 + k:
y = 4x^2 - 12x + 9 => y = 4(x^2 - 3x) + 9.
Now complete the square of x^2 - 3x: Take half of -3 and square the result, obtaining (-3/2)^2, or 9/4. Add 9/4 to x^2 - 3x and then subtract 9/4 from the result: We get x^2 - 3x + 9/4 - 9/4. Substitute this result back into
y = 4(x^2 - 3x) + 9: y = 4(x^2 - 3x + 9/4 - 9/4) + 9
and then rewrite the perfect square x^2 - 3 + 9/4 as the square of a binomial:
y = 4(x - 3/2)^2 - 9/4) + 9. This simplifies to:
y = 4(x - 3/2)^2 + 0.
Thus, the vertex is at (3/2, 0) and the axis of symmetry is x = 3/2. This agrees with Answer B.
Given : equation y = 4x^2 − 12x + 9
To Find :
A) The axis of symmetry is x = 0 and the vertex is (0,9).
B)The axis of symmetry is x= 1.5 and the vertex is (1.5, 0).
C)The axis of symmetry is x = 4 and the vertex is (4, -12).
D)The axis of symmetry is x = -1.5 and the vertex is (-1.5, 36).
Solution:
y = 4x² - 12x + 9
=> y = (2x)² - 2(2x)3 + 3²
=> y = (2x - 3)²
=> y = 4(x - 3/2)²
=> y = 4(x - 1.5)²
Axis of symmetry is x= 1.5
Vertex = (1.5 , 0)
The axis of symmetry is x= 1.5 and the vertex is (1.5, 0).
