Completing the Square for Quadratics
Read this topicExplanations 5
- (Video) Find the Turning Point of Quadratic Graphs by HEGARTYMATHS Here's a video by HEGARTYMATHS showing you how to use the method of completing the square to find the turning …
By Alex Federspiel, Anusha Rahman
- (Video) How to Find the Vertex of a Parabola by Nancy Pi In this video by Nancy Pi it is explained how to find the vertex of a parabola. There are two forms a parabola can come …
By Stefan Cuevas, Alex Federspiel, Anusha Rahman
- দ্বিঘাত ফাংশনের গ্রাফ দেখেছ? মানে y=ax2+bx+cy=ax^2+bx+cy=ax2+bx+c ফাংশনের গ্রাফ যেখানে a,b,c∈Ra,b,c\in\mathbb Ra,b,c∈R? এটি একটি parabola বা পরাবৃত্তের সমীকরণ। গ্রাফটা দেখতে অনে…
By Jubayer Nirjhor · বাংলা
- There are times in math when we want to convert a quadratic equation in standard from into other forms. For this lesson, we want to go from standard from to an equation with a p…
By Anusha Rahman
- Quadratics: Completing the Square In this lesson, we will learn how to complete the square to solve quadratic equations. You might remember that quadratic equations can look lik…
By Anusha Rahman
Problems 46
- What is the yyy-coordinate of the vertex of the parabola with equation y=x2+10x+142y=x^2+10x+142y=x2+10x+142?
- (Mathleague Team Round Problem, modified) Let n=2016!,n = 2016!,n=2016!, and define: Q=n2+n−1.Q = \sqrt{n^2+n-1}.Q=n2+n−1. Find the first 555 decimal places in the decimal repr…
- What is ccc?
- What value of ccc works?
- The vertex of y=(x−2)2+6y=(x-2)^2+6y=(x−2)2+6 is a point with coordinates (x1,y1)(x_1,y_1)(x1,y1). Compute 10x1+y110x_1 + y_110x1+y1.
- The vertex of y=x2+6x+18y=x^2+6x+18y=x2+6x+18 is (x1,y1)(x_1,y_1)(x1,y1). Compute x1+y1x_1 + y_1x1+y1.
- The vertex of y=x2−2x−9y=x^2-2x-9y=x2−2x−9 is a point with coordinates (x1,y1)(x_1,y_1)(x1,y1). Compute 10x1+y110x_1 + y_110x1+y1.
- The vertex of y=4x2+32x+53y=4x^2+32x+53y=4x2+32x+53 is (x1,y1)(x_1,y_1)(x1,y1). Compute x1⋅y1x_1\cdot y_1x1⋅y1.
- The vertex of y=x2+4x+6y=x^2+4x+6y=x2+4x+6 is (x1,y1)(x_1,y_1)(x1,y1). Compute x1+y1x_1 + y_1x1+y1.
- The vertex of y=9x2−54x+93y=9x^2-54x+93y=9x2−54x+93 is (x1,y1)(x_1,y_1)(x1,y1). Compute 100x1+y1100x_1 + y_1100x1+y1.
- Suppose f(x)=ax2+bx+cf(x) = ax^2+bx+cf(x)=ax2+bx+c is a quadratic such that f(x+1)−f(x)=4x+10f(x+1) - f(x) = 4x + 10f(x+1)−f(x)=4x+10 for all xxx, and the minimum value of fff i…
- What is the maximum value of 3x2+9x+173x2+9x+7\frac{3x^2+9x+17}{3x^2+9x+7}3x2+9x+73x2+9x+17 over all real numbers x?x?x? Source: ARML 1986
- A quadratic P(x)=ax2+bx+cP(x) = ax^2+bx+cP(x)=ax2+bx+c has roots at x=5x = 5x=5 and x=11x = 11x=11. What is the xxx-coordinate of the vertex of PPP?
- What is the minimum value of the quadratic x2+6x+17x^2 + 6x + 17x2+6x+17?
- Find the vertex of the quadratic polynomial (x+4)(x−2)(x+4)(x-2)(x+4)(x−2).
- If 8x2−12x+k8\frac{8x^2 - 12x + k}{8}88x2−12x+k is the square of a linear expression in xxx, find kkk.
- If the vertex of the parabola y=x2−12x+cy= x^2 - 12x + cy=x2−12x+c is on the xxx-axis, what is ccc?
- At what value of xxx does the quadratic function f(x)=(x−3)2+(x−5)2f(x) = (x-3)^2 + (x-5)^2f(x)=(x−3)2+(x−5)2 attain its minimum value?
- A spaceship is traveling around LV-426 to survey it. The navigational computer places the moon's center as the origin. The moon has a diameter of 216021602160 miles and the vert…
- Which coordinates below give the vertex of any quadratic function of the form y=ax2y=ax^2y=ax2?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function with a<0a<0a<0, what is the xxx-value of the vertex?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function with a<0a<0a<0, what is the yyy-value of the vertex?
- Hannah is selling homemade hats. So far, she has been selling the hats at 10\1010 per hat and typically sells 100100100 hats a week. \\ Hannah is a smart entrepreneur and she kn…
- Cassandra is selling cups of lemonade. So far, she has been selling each cup for 1\11 and typically sells 808080 cups a day. \\ Cassandra is a smart entrepreneur and she knows t…
- What is the axis of symmetry of the function f(x)=−2x2+4x−5f(x)=-2x^2+4x-5f(x)=−2x2+4x−5?
- What is the axis of symmetry of the function f(x)=−3x2−12x−8f(x)=-3x^2-12x-8f(x)=−3x2−12x−8?
- Concept check: to find the vertex of a quadratic function, we can write the equation in vertex form f(x)=a(x−h)2+kf(x)=a(x-h)^2+kf(x)=a(x−h)2+k. Which coordinates give the verte…
- Which of the following is the vertex of the function given by the rule f(x)=x2+12x+4f(x) = x^2+12x+4f(x)=x2+12x+4?
- Which of the following is the vertex of the parabola given by y=2x2+4x−8y = 2x^2+4x-8y=2x2+4x−8?
- Which of the following is the vertex of the graph of y=4x2+8x−12y = 4x^2+8x-12y=4x2+8x−12?
- Which of the following is the vertex of the parabola given by y=x2+6x−4y = x^2+6x-4y=x2+6x−4?
- Where is the bullet?
- How high is the drop? Hint: Can you factor this quadratic function? It might also help to visualize the function.
- Which of the following formulas will allow you to find the vertex of a quadratic function?
- You have two standard dice. On each, the sides with 111 and 666 are opposite, the sides with 222 and 555 are opposite, and the sides with 333 and 444 are opposite. You are playi…
- y(x)=a(x−h)2+ky(x) = a(x-h)^2 + ky(x)=a(x−h)2+k If a<0a < 0a<0, what is the vertex of yyy's parabola? Is it a minimum point or maximum point?
- y(x)=a(x−h)2+ky(x) = a(x-h)^2 + ky(x)=a(x−h)2+k If a>0a > 0a>0, what is the vertex of yyy's parabola? Is it a minimum point or maximum point?
- y(x)=a(x+h)2+ky(x) = a(x+h)^2 + ky(x)=a(x+h)2+k If a>0a > 0a>0, what is the vertex of yyy's parabola? Is it a minimum point or maximum point?
- y(x)=a(x+h)2+ky(x) = a(x+h)^2 + ky(x)=a(x+h)2+k If a<0a < 0a<0, what is the vertex of yyy's parabola? Is it a minimum point or maximum point?
- y=2(x−1)2+3y = 2(x-1)^2+3y=2(x−1)2+3 What is the vertex of function yyy's parabola?
- y=3(x−2)2+1y = 3(x-2)^2+1y=3(x−2)2+1 What is the xxx-coordinate of the parabola's vertex?
- y=(x+3)2−2y = (x+3)^2-2y=(x+3)2−2 What is the yyy-coordinate of the parabola's vertex?
- Let xxx and yyy be real numbers such that x2+y2−22x−16y+113=0x^2 + y^2 - 22x - 16y + 113 = 0x2+y2−22x−16y+113=0. Determine the smallest possible value of xxx. Source: Lexington …
- Factor x2+10x−y2−2y+24x^2 + 10x - y^2 - 2y + 24x2+10x−y2−2y+24.
- If a parabola passes through the points (2,0)(2, 0)(2,0) and (3,1),(3, 1),(3,1), how many possible locations are there for the vertex of the parabola?
- The circle with equation (x−1)2+y2=4(x - 1)^2 + y^2 = 4(x−1)2+y2=4 intersects the parabola y=x2−2x+3y = x^2 - 2x + 3y=x2−2x+3 in one location on the real xyxyxy plane. Which of …