Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Complete the square to re-write the quadratic function in vertex form: y=x^(2)+9x+7 Answer: y=

Complete the square to re-write the quadratic function in vertex form:\newliney=x2+9x+7 y=x^{2}+9 x+7 \newlineAnswer: y= y=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Write a quadratic function in vertex formright chevron icon

Full solution

Q. Complete the square to re-write the quadratic function in vertex form:\newliney=x2+9x+7 y=x^{2}+9 x+7 \newlineAnswer: y= y=
  1. Identify vertex form: Identify the vertex form of a parabola.\newlineThe vertex form of a parabola is given by y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola.
  2. Complete the square: Begin completing the square for the equation y=x2+9x+7y = x^2 + 9x + 7.\newlineTo complete the square, we need to form a perfect square trinomial from the quadratic and linear terms. We do this by adding and subtracting (b2)2(\frac{b}{2})^2, where bb is the coefficient of xx.
  3. Calculate (b/2)2(b/2)^2: Calculate (b/2)2(b/2)^2 where bb is the coefficient of xx, which is 99 in this case.\newline(b/2)2=(9/2)2=81/4(b/2)^2 = (9/2)^2 = 81/4\newlineWe will add and subtract this value to the equation.
  4. Add/subtract (b/2)2(b/2)^2: Add and subtract (b/2)2(b/2)^2 to the equation y=x2+9x+7y = x^2 + 9x + 7.\newliney=x2+9x+814−814+7y = x^2 + 9x + \frac{81}{4} - \frac{81}{4} + 7
  5. Rewrite equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. \newliney=(x2+9x+814)−814+7y = (x^2 + 9x + \frac{81}{4}) - \frac{81}{4} + 7
  6. Factor and simplify: Factor the perfect square trinomial and simplify the constants.\newliney=(x+92)2−814+284y = (x + \frac{9}{2})^2 - \frac{81}{4} + \frac{28}{4}\newliney=(x+92)2−534y = (x + \frac{9}{2})^2 - \frac{53}{4}

More problems from Write a quadratic function in vertex form

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 8 months ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 5 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 5 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 5 months ago

View all (90)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant