Question

Convert the following function from standard form to vertex form f(x) = x^2 + 7x - 1

88

likes
442 views

Answer to a math question Convert the following function from standard form to vertex form f(x) = x^2 + 7x - 1

Expert avatar
Maude
4.7
46 Answers
To convert the function f(x) = x^2 + 7x - 1 from standard form to vertex form, we need to complete the square. The vertex form of a quadratic function is: f(x) = a(x - h)^2 + k where (h, k) is the vertex of the parabola. To complete the square, we add and subtract (b/2a)^2 to the standard form of the quadratic function, where a is the coefficient of the x^2 term, and b is the coefficient of the x term. This gives us: f(x) = x^2 + 7x - 1 + (49/4) - (49/4) Now, we can group the x terms and factor the first three terms: f(x) = (x^2 + 7x + (49/4)) - (49/4) - 1 Next, we can write the first three terms as a square of a binomial: f(x) = (x + (7/2))^2 - (49/4) - 1 Finally, we can simplify the expression by combining the constant terms: f(x) = (x + (7/2))^2 - (53/4) Therefore, the function f(x) = x^2 + 7x - 1 in vertex form is: f(x) = (x + (7/2))^2 - (53/4)

Frequently asked questions (FAQs)
Math question: Find the length of side a in a triangle where angle C is 40°, side b is 8, and angle A is 90°. (
+
Find the measure of angle ABC if angle EFD is 30° and angle BCD is twice the measure of angle EFD.
+
What is the value of √(64)^2 - 4√(9^2) + √(5^2) - 2√(16^2)?
+
New questions in Mathematics
calculate the following vector based on its base vectors a= -18i,26j
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
A client did not advance L 10,000 for the rental of a parking area and it corresponds to 4 months, of which 2 months were consumed
A, B, C and D are numbers; If ABCD = 23, What is the result of ABCD BCDA CDAB DABC operation?
7273736363-8
Director of reservations believes that 9% of the ticketed passengers are no-shows. If the directors right what is the probability that the proportion of no-shows in a sample of 789 ticketed passengers with differ from the population proportion buy more than 3% round your answer to four decimal places.
Determine the minimum degree that an algebraic equation can assume knowing that it admits 2 as a double root and -i as a triple root
Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point (0,−2)
In a order to compare the means of two populations, independent random samples of 410 observations are selected from each population, with Sample 1 the results found in the table to the right. Complete parts a through e below. X1 = 5,319 S1= 143 a. Use a 95% confidence interval to estimate the difference between the population means (H - H2) Interpret the contidence interval. The contidence interval IS (Round to one decimal place as needed.) Sample 2 X2 = 5,285 S2 = 198 Aa. Use a 95% confidence interval to estimate the difference between the population means (A1 - M2) Interpret the contidence interval. The contidence interval Is (Round to one decimal place as needed.) b. Test the null hypothesis Ho versus alternative hypothesis Ha (H What is the test statistic? H2) + Give the significance level of the test, and interpret the result. Use a = 0.05. Z=
A box of numbered pens has 12 red, 12 blue, 12 green and 12 yellow pens. The pens for each colour are numbered from 1 to 12. There is a unique number on each pen, so no pen is exactly the same as any other pen in the box. When reaching into the box to randomly draw five pens without replacement, what is the proportion of getting exactly four pens of the same colour (Note: the numbers matter but the order does not)?
User One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s(t), this function s is called the clockwise function of the movement. By deriving the time function we obtain the velocity function at time t, denoted by v(t). A body has a time function that determines its position in meters at time t as S(t)=t.³√t+2.t . Present the speed of this body at time t = 8 s.
A loan is repaid with payments of $2226 made at the end of each month for 12 years. If interest on the loan is 5.2%, compounded semi-annually, what is the initial value of the loan? Enter to the nearest cent (two decimals). Do not use $ signs or commas.
How to factorise 5y^2 -7y -52
Given a circle 𝑘(𝑆; 𝑟 = 4 𝑐𝑚) and a line |𝐴𝐵| = 2 𝑐𝑚. Determine and construct the set of all centers of circles that touch circle 𝑘 and have radius 𝑟 = |𝐴𝐵|
Farm Grown, Inc., produces cases of perishable food products. Each case contains an assortment of vegetables and other farm products. Each case costs $5 and sells for $15. If there are any not sold by the end of the day, they are sold to a large food processing company for $3 a case. The probability that daily demand will be 100 cases is 0.30, the probability that daily demand will be 200 cases is 0.40, and the probability that daily demand will be 300 cases is 0.30. Farm Grown has a policy of always satisfying customer demands. If its own supply of cases is less than the demand, it buys the necessary vegetables from a competitor. The estimated cost of doing this is $16 per case. (a) Draw a decision table for this problem (b) What do you recommend?
0<x<2π aralığındaki f(x)=x÷2 fonksiyonunun 0 < x < 4π için grafiğini çiziniz ve 0<x<2n için Fourier seri dönüşümünü gerçekleştiriniz.
What is the percentage of nitrogen abundance in copper dinatrate Cu(NO3)2
the product of a 2-digit number and a 3-digit number is about 50000, what are these numbers
Determine the general solution of the equation y′+y=e−x .
answer this math question The scale on a map is drawn so that 5.5 inches corresponds to an actual distance of 225 miles. If two cities are 12.75 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) miles apart. The two cities are how many miles apart