Question

For all real numbers $a$, $b$, and $c$ such that $a \not = 0$, $x = \dfrac{-b}{2a}$ is a maximiser of the function $f(x) = ax^2 + bx + c$?

score 29 · Answer 1 · 2017-02-03 04:07:06

29

Views

For all real numbers $a$, $b$, and $c$ such that $a \not = 0$, $x = \dfrac{-b}{2a}$ is a maximiser of the function $f(x) = ax^2 + bx + c$?

Published on 03 Feb 2017 - 4:07

score 138 · Answer 2 · 2017-02-03 05:18:56

138

Views

Prove that, if $x^∗ = \dfrac{−b}{2a}$ is a maximizer of the function $f(x) = ax^2 + bx + c$, then a < 0.

Published on 03 Feb 2017 - 5:18

score 301 · Answer 3 · 2026-04-06 12:19:09

301

Views

Two ellipses with foci on $x$-axis each travels through the center of the other

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score 281 · Answer 4 · 2017-02-04 07:46:42

281

Views

What is $x$, if $3^x+3^{-x}=1$?

Published on 04 Feb 2017 - 7:46

score 61 · Answer 5 · 2026-03-31 22:42:49

61

Views

Methods for solving a quadratic equation.

Published on 31 Mar 2026 - 22:42

score 314 · Answer 6 · 2017-02-04 19:35:23

314

Views

Simple Questions about Quadratic equations with 2 variables.

Published on 04 Feb 2017 - 19:35

score 116 · Answer 7 · 2017-02-05 07:59:18

116

Views

Show that line $kx - y + 2 - k = 0$ is NOT tangent to the circle $x^2 + y^2 = 9$ for any value of $k$

Published on 05 Feb 2017 - 7:59

score 1.3k · Answer 8 · 2017-02-05 21:29:38

1.3k

Views

Complex Numbers Quadratics

Published on 05 Feb 2017 - 21:29

score 83 · Answer 9 · 2026-04-06 13:43:59

83

Views

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score 2k · Answer 10 · 2017-02-07 18:21:17

2k

Views

For the statement A implies B, write the statement NOT B implies NOT A.

Published on 07 Feb 2017 - 18:21

score 2k · Answer 11 · 2017-02-08 11:12:12

2k

Views

Find minimal value of $abc$ if the quadratic equation $ax^2-bx+c = 0$ has two roots in $(0,1)$

Published on 08 Feb 2017 - 11:12

score 512 · Answer 12 · 2026-03-29 17:25:16

512

Views

finding the inverse function with an absolute value present

Published on 29 Mar 2026 - 17:25

score 1.6k · Answer 13 · 2026-04-02 00:24:05

1.6k

Views

Prove, by contradiction, that, if $cx^2 + bx + a$ has no rational root, then $ax^2 + bx + c$ has no rational root.

Published on 02 Apr 2026 - 0:24

score 3k · Answer 14 · 2017-02-11 07:02:31

3k

Views

Can the quadratic formula be used with variable coefficients?

Published on 11 Feb 2017 - 7:02

score 166 · Answer 15 · 2026-03-29 04:48:01

166

Views

How to solve for $x$ algebraically, given that $x^2 = 4- \sqrt{12}$

Published on 29 Mar 2026 - 4:48

List Question

For all real numbers $a$, $b$, and $c$ such that $a \not = 0$, $x = \dfrac{-b}{2a}$ is a maximiser of the function $f(x) = ax^2 + bx + c$?

Prove that, if $x^∗ = \dfrac{−b}{2a}$ is a maximizer of the function $f(x) = ax^2 + bx + c$, then a < 0.

Two ellipses with foci on $x$-axis each travels through the center of the other

What is $x$, if $3^x+3^{-x}=1$?

Methods for solving a quadratic equation.

Simple Questions about Quadratic equations with 2 variables.

Show that line $kx - y + 2 - k = 0$ is NOT tangent to the circle $x^2 + y^2 = 9$ for any value of $k$

Complex Numbers Quadratics

System of equations - conics

For the statement A implies B, write the statement NOT B implies NOT A.

Find minimal value of $abc$ if the quadratic equation $ax^2-bx+c = 0$ has two roots in $(0,1)$

finding the inverse function with an absolute value present

Prove, by contradiction, that, if $cx^2 + bx + a$ has no rational root, then $ax^2 + bx + c$ has no rational root.

Can the quadratic formula be used with variable coefficients?

How to solve for $x$ algebraically, given that $x^2 = 4- \sqrt{12}$

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