The curve \(y=2x^2+3x-9\) undergoes a parallel translation by \(7\) units in the positive direction of the \(x\)-axis and \(-3\) units in the positive direction of the \(y\)-axis. If the equation of the resulting curve is \(y=ax^2+bx+c,\) what is \(a+b+c?\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!

Consider a translation of axes
\[T: (x, y) \to (x+a, y+b)\]
such that the coordinates of a point \(P=(7, 4)\) with respect to the new system of coordinates after translation are \(P'=(10,-11).\) What is the value of \(a+b?\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!

If the point \((m,n)\) is shifted by \(6\) in the positive \(x\) direction and by \(-12\) in the positive \(y\) direction, then it coincides with the center of the circle \[x^2+y^2-6x+2y-13=0.\] What is the value of \(m+n?\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!