Question

Which equation below has an axis of symmetry of x = 4 over 3?

Answer 1

. y = −3x2 − 4x + 5
b. y = −3x2 + 4x + 5
c. y = −3x2 − 8x − 1
d. y = −3x2 + 8x − 1

Answer 2

\[y=-3x^2+8x-1=-3\left( x^2-\frac{ 8 }{ 3 }x+\left( \frac{ 4 }{ 3 } \right)^2-\left( \frac{ 4 }{ 3 } \right)^2 \right)-1\]
\[=-3\left( x-\frac{ 4 }{ 3 } \right)^2+3 \times \frac{ 16 }{ 9 }-1\]
\[=-3\left( x-\frac{ 4 }{ 3 } \right)^2+\frac{ 13 }{ 3 }\]
\[x-\frac{ 4 }{ 3 }=0,gives~x=\frac{ 4 }{ 3 }\]

Answer 3

Your axis of symmetry is the vertical line given by x=4/3. Important: Please note that this x value also represents the x-coordinate of the vertex.

Note, also, that the formula for the x-coordinate of the vertex of y=ax^2 + bx + c is
x=-b/(2a). You can equate this to the actual value, which is x=4/3.

Set these two equations = to each other. Note that a is the same (-3) in all four given equations. Use your equation (above) to calculate b.