maximum

260 Questions
128 Answers

0

135

0

+834

help plz

Find the vertex of the graph of the equation $x - y^2 + 8y = 13 + 2y + y^2 - 7y - 14$.

maximum 21.11.2023

0

150

0

+834

how to find vertex

Find the vertex of the graph of the equation y = -2x^2 + 8x + 15 - 3x^2 + 7x - 25

maximum 21.11.2023

0

148

0

+834

area of a circle

Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$.

maximum 21.11.2023

0

117

0

+834

help algebra

The graph of $y = ax^2 + bx + c$ has an axis of symmetry of $x = -1.$ If $a = 2,$ then find $b.$

maximum 21.11.2023

0

139

0

+834

parabola

Graph a parabola with axis of symmetry $x = 3,$ an $x$-intercept at $x = -8,$ and $y$-intercept $5.$

maximum 21.11.2023

0

103

1

+834

quadratic

Let c be a real number, and consider the system of quadratic equations
y = x^2 - 9x + c,
y = 8x^2 - 13x.
For which values of c does this system have:
(a) Exactly one real solution (x,y)?
(b) More than one real solution?
(c) mehr ..

maximum 20.11.2023

0

81

1

+834

help with algebra

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}

maximum 11.11.2023

0

98

1

+834

complex numbers

Compute (1 + i)/(2 - i)(3 + i).

maximum 11.11.2023

0

124

2

+834

plz help

The real numbers $a$ and $b$ satisfy $a - b = 1$ and $a^3 - b^3 = 1.$
(a) Find all possible values of $ab.$
(b) Find all possible values of $a + b.$
(c) Find all possible values of $a$ and $b.$

maximum 11.11.2023

0

148

0

+834

help with roots

Let $a$ and $b$ be the roots of the quadratic $2x^2 - 8x + 7 = -3x^2 + 5x + 11.$ Compute $a^3/b^2 + b^3/a^2.$

maximum 11.11.2023

+834

-1

Do not post AoPS homework.

maximum20.01.2025