f(x) = 2x2 – x + 1
f(x) = x2 + 2x – 1
f(x) = x2 – 2x + 1
we know that
The equation of the vertical parabola in vertex form is equal to
where
(h,k) is the vertex
The axis of symmetry is equal to the x-coordinate of the vertex
so
------> axis of symmetry of a vertical parabola
we will determine in each case the axis of symmetry to determine the solution
case A)
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Factor the leading coefficient
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
the vertex is the point
the axis of symmetry is
therefore
the function has an axis of symmetry at
case B)
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Factor the leading coefficient
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
the vertex is the point
the axis of symmetry is
therefore
the function does not have a symmetry axis in
case C)
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
the vertex is the point
the axis of symmetry is
therefore
the function does not have a symmetry axis in
case D)
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
the vertex is the point
the axis of symmetry is
therefore
the function does not have a symmetry axis in
the answer is
Choose all answers that are correct.
A.Use logical reasoning.
Multiply 1,200 by 2 to figure out how many candles were made in June and July. Multiply 1,345 by 2 to figure out how many candles were made in August and September. Add the two numbers together to find the total number of candles made in four months.
B.Draw a diagram.
Draw two circles. In one circle write 1,200 and in the other circle write 1,345. Add the numbers in the circles together.
C.Work backward.
Divide 1,200 by 2 (for the 2 months, June and July). Then divide 1,345 by 2 (for the 2 months August and September). Add these two numbers.
D.Translate into an equation.
1,200 × 2 + 1,345 × 2 = c
-9,-16,-23,-30,-37,-44