Mathematics
Grade 11
15 min
Find the vertix of the parabola
Find the vertix of the parabola
What you'll learn
- Identify the fraction of a whole number when shown a visual model (e.g., circles divided into equal parts) with 80% accuracy.
- Solve for a fraction of a number (1/2, 1/3, 1/4) using manipulatives (e.g., counters, blocks) to find the answer to at least 3 out of 4 word problems.
- Explain, using words and/or pictures, how to find one half of a number in at least two different ways.
- Apply the concept of fractions to divide a set of objects into equal groups as described in a word problem, achieving a correct answer in 4 out of 5 attempts.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Identify the vertex of a parabola directly from its vertex form, y = a(x - h)^2 + k.
Calculate the coordinates of the vertex from the general quadratic form, y = ax^2 + bx + c, using the formula x = -b/(2a).
Convert a quadratic equation from general form to vertex form by completing the square.
Distinguish between vertical and horizontal parabolas and find their respective vertices.
Determine whether the vertex represents a maximum or minimum point of the parabola based on its orientation.
Apply the concept of the vertex to solve problems involving projectile motion and optimization.
Ever wondered about the highest point a basketball reaches in a perfect shot? 🏀 That peak point is the vertex of a parabolic path!
This tutorial will teach you three powerf...
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Key Concepts & Vocabulary
TermDefinitionExample
ParabolaA U-shaped curve representing a quadratic function. It is the set of all points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).The graph of the equation y = x^2 is a simple parabola that opens upwards with its vertex at the origin (0, 0).
VertexThe point where the parabola changes direction. It is the minimum point if the parabola opens upwards or the maximum point if it opens downwards.For the parabola y = (x - 2)^2 + 1, the vertex is at the point (2, 1).
Axis of SymmetryA vertical or horizontal line that passes through the vertex and divides the parabola into two mirror-image halves.For y = x^2 + 4x + 5, the axis of symmetry is the vertical line x = -2, which passes through its vertex (-2, 1).
Vertex Form (Ve...
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Core Formulas
Vertex Form Formula
For a parabola in the form y = a(x - h)^2 + k, the vertex is at the point (h, k).
Use this when the equation is already in vertex form. Simply identify the values of 'h' and 'k'. Be careful with the sign of 'h'.
General Form Vertex Formula
For a parabola in the form y = ax^2 + bx + c, the x-coordinate of the vertex is given by x = -b / (2a).
Use this formula to find the x-coordinate of the vertex. To find the y-coordinate, substitute this x-value back into the original equation.
Horizontal Parabola Vertex Form
For a parabola in the form x = a(y - k)^2 + h, the vertex is at the point (h, k).
This is for parabolas that open sideways. Notice that 'h' is the x-coordinate and 'k' is associated with the...
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Challenging
A farmer has 100 meters of fencing to enclose a rectangular plot of land on three sides, with a straight river forming the fourth side. The area of the plot is given by the function A(x) = -2x^2 + 100x, where x is the length of the side perpendicular to the river. What is the vertex of this area function, representing the dimension and maximum area?
A.(50, 0)
B.(25, 1250)
C.(100, -10000)
D.(25, 50)
Challenging
A parabola of the form y = ax^2 + bx + c passes through the points (0, 5), (1, 6), and (2, 11). What is the vertex of this parabola?
A.(1/2, 23/4)
B.(1/4, 39/8)
C.(-1/4, 41/8)
D.(1, 6)
Challenging
For any parabola in the general form y = ax^2 + bx + c, the y-coordinate of the vertex can be expressed in terms of the coefficients a, b, and c. What is this expression?
A.(b^2 - 4ac) / 4a
B.c - b^2 / (2a)
C.(4ac - b^2) / 4a
D.c
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Frequently asked questions
What grade level is "Find the vertix of the parabola"?
Find the vertix of the parabola is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the vertix of the parabola?
You'll be able to: Identify the fraction of a whole number when shown a visual model (e.g., circles divided into equal parts) with 80% accuracy; Solve for a fraction of a number (1/2, 1/3, 1/4) using manipulatives (e.g., counters, blocks) to find….
Is "Find the vertix of the parabola" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Find the vertix of the parabola?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.