Mathematics, 30.08.2019 07:30 Undrea43

The graph of which function has an axis of symmetry at x =-1/4 ?
f(x) = 2x2 + x – 1
f(x) = 2x2 – x + 1
f(x) = x2 + 2x – 1
f(x) = x2 – 2x + 1

Answers: 2

Show answers

Answers

Answer from: glitch14

The graph of which function has an axis of symmetry at x = -1/4 is :

f(x) = 2x² + x – 1Further explanation

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

Let us now tackle the problem!

An axis of symmetry of quadratic equation y = ax² + bx + c is :

$\large {\boxed {x = \frac{-b}{2a} } }$

Option 1 :

f(x) = 2x² + x – 1 → a = 2 , b = 1 , c = -1

Axis of symmetry → $x = \frac{-b}{2a} = \frac{-1}{2(2)} = -\frac{1}{4}$

Option 2 :

f(x) = 2x² – x + 1 → a = 2 , b = -1 , c = 1

Axis of symmetry → $x = \frac{-b}{2a} = \frac{-(-1)}{2(2)} = \frac{1}{4}$

Option 3 :

f(x) = x² + 2x – 1 → a = 1 , b = 2 , c = -1

Axis of symmetry → $x = \frac{-b}{2a} = \frac{-2}{2(1)} = -1$

Option 4 :

f(x) = x² – 2x + 1 → a = 1 , b = -2 , c = 1

Axis of symmetry → $x = \frac{-b}{2a} = \frac{-(-2)}{2(1)} = 1$

Learn moreSolving Quadratic Equations by Factoring : Determine the Discriminant : Formula of Quadratic Equations : Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number

The graph of which function has an axis of symmetry at x =-1/4 ? f(x) = 2x2 + x – 1 f(x) = 2x2 – x

Answer from: IntellTanito

The graph of function $\boxed{f(x)=2x^{2}+x-1}$ has an axis of symmetry as $\boxed{x=-\frac{1}{4}}$ .

Further explanation:

The standard form of a quadratic equation is as follows:

$\boxed{f(x)=ax^{2}+bx+c}$

The vertex form of a quadratic equation is as follows:

$\boxed{g(x)=a(x-h)^{2}+k}$

Axis of symmetry is the line which divides the graph of the parabola in two perfect halves.

The formula for axis of symmetry of a quadratic function is given as follows:

$\boxed{x=-\dfrac{b}{2a}}$

The first function is given as follows:

$f(x)=2x^{2}+x-1$

The above function is in standard form with a=2 , b=1 and c=-1 .

Then its axis of symmetry is calculated as,

$\begin{aligned}x&=-\dfrac{b}{2a}\\&=-\dfrac{1}{2\times2}\\&=-\dfrac{1}{4}\end{aligned}$

The axis of symmetry of first function is $x=-\frac{1}{4}$ .

Express the function $f(x)=2x^{2}+x-1$ in its vertex form,

$\begin{aligned}f(x)&=2x^{2}+x-1\\&=(\sqrt{2}x)^{2}+\left(2\times \sqrt{2}x\times \dfrac{1}{2\sqrt{2}}\right)-1+\left(\dfrac{1}{2\sqrt{2}}\right)^{2}-\left(\dfrac{1}{\sqrt{2}}\right)^{2}\\&=\left(\sqrt{2}x+\dfrac{1}{2\sqrt{2}}\right)^{2}-1-\dfrac{1}{8}\\&=\left[\sqrt{2}\left(x+\dfrac{1}{4}\right)\right]^{2}-\dfrac{9}{8}\\&=2\left(x-\left(-\dfrac{1}{4}\right)\right)^{2}-\dfrac{9}{8}\end{aligned}$

The above equation is in the vertex form with a=2 , $h=-\dfrac{1}{4}$ and $k=-\dfrac{9}{8}$ .

Therefore, its axis of symmetry is given as,

$\begin{aligned}x&=h\\x&=-\dfrac{1}{4}\end{aligned}$

The graph of function $f(x)=2x^{2}+x-1$ is shown in Figure 1.

The second function is given as follows:

$f(x)=2x^{2}-x+1$

The above function is in standard form with a=2 , b=-1 and c=1 .

Then its axis of symmetry is calculated as,

$\begin{aligned}x&=-\dfrac{b}{2a}\\&=-\dfrac{(-1)}{2\times2}\\&=\dfrac{1}{4}\end{aligned}$

The axis of symmetry of second function is $x=\frac{1}{4}$ .

The third function is given as follows:

$f(x)=x^{2}+2x-1$

The above function is in standard form with a=1 , b=2 and c=-1 .

Then its axis of symmetry is calculated as,

$\begin{aligned}x&=-\dfrac{b}{2a}\\&=-\dfrac{2}{2\times1}\\&=-1\end{aligned}$

The axis of symmetry of third function is x=-1 .

The fourth function is given as follows:

$f(x)=x^{2}-2x+1$

The above function is in standard form with a=1 , b=-2 and c=1 .

Then its axis of symmetry is calculated as,

$\begin{aligned}x&=-\dfrac{b}{2a}\\&=-\dfrac{-2}{2\times1}\\&=1\end{aligned}$

The axis of symmetry of fourth function is x=1 .

Therefore, the function $\boxed{f(x)=2x^{2}+x-1}$ has an axis of symmetry as $\boxed{x=-\frac{1}{4}}$ .

Learn more:

1. A problem on graph

2. A problem on function

3. A problem on axis of symmetry

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Functions

Keywords:Graph, function, axis, f(x), 2x^2+x-1, axis of symmetry, symmetry, vertex, perfect halves, graph of a function, x =- 1/4.

Answer from: Quest

knlknlkkn

step-by-step explanation:

Answer from: Quest

see explanation

step-by-step explanation:

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

remove brackets and collect like terms

13 - $\frac{3}{2}$ r - 1 + r

= 12 - $\frac{1}{2}$ r

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

remove brackets and collect like terms

= 7r - $\frac{3}{2}$ - $\frac{2}{3}$ - 6r

[- $\frac{3}{2}$ - $\frac{2}{3}$ = - $\frac{9}{6}$ - $\frac{4}{6}$ = - $\frac{13}{6}$ ]

= r - $\frac{13}{6}$

Questions in other subjects:

Mathematics, 10.04.2020 22:56

Match each function with a key aspect of its graph...

Mathematics, 10.04.2020 22:56

Give the equation of the line perpendicular to the line through (3, 2) and (-2, 4) thatpasses through the point (1, 1)....

Biology, 10.04.2020 22:56

Does a moving magnetic field creat a megnetic field...

Mathematics, 10.04.2020 22:56

Pythagorean Theorem Converse A right triangle has sides of length 3 cm and 4 cm. What is the length of its hypotenuse? A triangle has sides of

English, 10.04.2020 22:56

WHAT IS THE ERROR JUST NINTEY SENSE FOR A BAG...

Biology, 10.04.2020 22:56

Could two communities with different characteristics live in one place? Explain your answer...

English, 10.04.2020 22:56

Imagine that you are recalling a conversation you recently had with someone concerning an interesting event in your hometown. You cannot remember the details of the event, but you...

Business, 10.04.2020 22:56

On January 1, 2017, Dawson, Incorporated, paid $100,000 for a 30% interest in Sacco Corporation. This investee had assets with a book value of $550,000 and liabilities of $300,000....

Physics, 10.04.2020 22:56

Find whether the following transitions (specified in terms of the initial and final quantum numbers n, ?, m?, and ms) are allowed, and if they are, find the energy involved and whe...

History, 10.04.2020 22:56

SOMEONE PLEASE HELP!! Which statement is true about Richard Nixon and Lyndon Johnson’s social and economic policies? A. Johnson focused his spending on national...

More questions: Mathematics Another questions

The graph of which function has an axis of symmetry at x =-1/4 ? f(x) = 2x2 + x – 1 f(x) = 2x2 – x + 1 f(x) = x2 + 2x – 1 f(x) = x2 – 2x + 1

Answers

Other questions on the subject: Mathematics

Questions in other subjects:

The graph of which function has an axis of symmetry at x =-1/4 ?
f(x) = 2x2 + x – 1
f(x) = 2x2 – x + 1
f(x) = x2 + 2x – 1
f(x) = x2 – 2x + 1