Symbol

# Calculator search results

Formula
Convert to the standard form of the quadratic function
Find the maximum and minimum of the quadratic function
Calculate the differentiation
Graph
$y = - x ^ { 2 } - 3 x + 10$
$x$Intercept
$\left ( - 5 , 0 \right )$, $\left ( 2 , 0 \right )$
$y$Intercept
$\left ( 0 , 10 \right )$
$y = -x ^{ 2 } -3x+10$
$y = - \left ( x + \dfrac { 3 } { 2 } \right ) ^ { 2 } + \dfrac { 49 } { 4 }$
Rewrite it as the standard form of the quadratic function
$y = \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } + 10$
 In order to convert the quadratic equation on the right side to the standard form, enclose it with the coefficient of the highest term 
$y = \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ x } \right ) + 10$
$y = - \left ( x ^ { 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 3 \right ) x \right ) + 10$
 Simplify Minus 
$y = - \left ( x ^ { 2 } + 3 x \right ) + 10$
$y = - \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) + 10$
 Add and subtract constants to convert the quadratic equation on the right side to the standard form 
$y = - \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \left ( \color{#FF6800}{ \dfrac { 3 } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ \dfrac { 3 } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \right ) + 10$
$y = - \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \left ( \color{#FF6800}{ \dfrac { 3 } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( \dfrac { 3 } { 2 } \right ) ^ { 2 } \right ) + 10$
 Organize the expression using $A^{2} ± 2AB + B^2 = (A ± B)^{2}$
$y = - \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( \dfrac { 3 } { 2 } \right ) ^ { 2 } \right ) + 10$
$y = - \left ( \left ( x + \dfrac { 3 } { 2 } \right ) ^ { 2 } - \left ( \color{#FF6800}{ \dfrac { 3 } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \right ) + 10$
 Calculate power 
$y = - \left ( \left ( x + \dfrac { 3 } { 2 } \right ) ^ { 2 } - \color{#FF6800}{ \dfrac { 9 } { 4 } } \right ) + 10$
$y = \color{#FF6800}{ - } \left ( \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 9 } { 4 } } \right ) + 10$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$y = \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ \dfrac { 9 } { 4 } } + 10$
$y = - \left ( x + \dfrac { 3 } { 2 } \right ) ^ { 2 } + \color{#FF6800}{ \dfrac { 9 } { 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
 Add two numbers $\dfrac { 9 } { 4 }$ and $10$
$y = - \left ( x + \dfrac { 3 } { 2 } \right ) ^ { 2 } + \color{#FF6800}{ \dfrac { 49 } { 4 } }$
$\dfrac { 49 } { 4 }$
Find the maximum and minimum of the quadratic function
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
 Rewrite it as the standard form of the quadratic function 
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 49 } { 4 } }$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 49 } { 4 } }$
 As $a \lt 0$ is, the maximum value is $\dfrac { 49 } { 4 }$ if $x$ = $- \dfrac { 3 } { 2 }$
$\color{#FF6800}{ \dfrac { 49 } { 4 } }$
$\dfrac {d } {d x } {\left( y \right)} = - 2 x - 3$
Calculate the differentiation of the logarithmic function
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right)}$
 Calculate the differentiation 
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
Have you found the solution you wanted?
Try again
Try more features at Qanda!
Search by problem image
Ask 1:1 question to TOP class teachers
AI recommend problems and video lecture