y=−3x^2−4x+1
(a) Write the equation of the parabola in standard form
it wants the answer like:
y= .....(x +-.....)^2...+-......
thank you
yes! thank you, Scott!!!!!!!!!!!!!!!!!!!!
factoring ... y = -3 (x^2 + 4/3 x - 1/3)
completing the square ... y = -3 {[(x + 2/3)^2 - 4/9] - 1/3}
combining constants ... y = -3 (x + 2/3)^2 + 1/3
correction ... sorry
combining constants ... y = -3 (x + 2/3)^2 + 7/3
To rewrite the equation of the parabola in standard form, we need to complete the square.
Given: y = -3x^2 - 4x + 1
Step 1: Group the terms involving x^2 and x together.
y = (-3x^2 - 4x) + 1
Step 2: Factor out the common factor (if any) in the terms involving x^2 and x.
y = -x(3x + 4) + 1
Step 3: To complete the square, take half of the coefficient of x and square it, then add this value and subtract it inside the parentheses.
y = -x(3x + 4) + 1 - [(4/2)^2]
Simplifying further:
y = -x(3x + 4) + 1 - 4
Step 4: Simplify the equation.
y = -x(3x + 4) - 3
Finally, let's rewrite the equation in the standard form:
y = -(3x + 4)^2 - 3