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A parabola opening up or down has vertex $(0,0)$ and passes through $(2,-1)$ . Write its equation in vertex form. $\newline$ Simplify any fractions.

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Write a quadratic function from its vertex and another point

Full solution

Q. A parabola opening up or down has vertex

(0,0)

and passes through

(2,-1)

. Write its equation in vertex form.

\newline

Simplify any fractions.

Vertex Form: What is the vertex form of the parabola? $\newline$ Vertex form of parabola: $y = a(x - h)^2 + k$
Equation at ( $0$ , $0$ ): What is the equation of a parabola with a vertex at $(0, 0)$ ? $\newline$ Substitute $0$ for $h$ and $0$ for $k$ in vertex form. $\newline$ $y = a(x - 0)^2 + 0$ $\newline$ $y = ax^2$
Substitute Values: $y = ax^2$ $\newline$ Replace the variables with $(2, -1)$ in the equation. $\newline$ Substitute $2$ for $x$ and $-1$ for $y$ . $\newline$ $-1 = a(2)^2$ $\newline$ $-1 = 4a$
Solve for $a$ : $-1 = 4a$ $\newline$ Solve for $a$ . $\newline$ $-\frac{1}{4} = a$
Equation with $a = -\frac{1}{4}$ : $y = ax^2$ $\newline$ What is the equation of the parabola if $a = -\frac{1}{4}$ ? $\newline$ Substitute $-\frac{1}{4}$ for $a$ . $\newline$ $y = (-\frac{1}{4})x^2$ $\newline$ Vertex form of parabola: $y = -\frac{1}{4}x^2$

More problems from Write a quadratic function from its vertex and another point

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 8 months ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

Posted 7 months ago

Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

\newline

\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

Posted 5 months ago

Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

Posted 5 months ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Posted 5 months ago

Question

h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

Posted 5 months ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Posted 5 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 4 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 4 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 5 months ago

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Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant