Mathematics
Grade 11
15 min
Write equations of parabolas in vertex form using properties
Write equations of parabolas in vertex form using properties
What you'll learn
- Identify the unit fractions that make up a given fraction (e.g., recognize that 3/4 is made up of 3 fractions of 1/4).
- Represent a fraction as the sum of unit fractions using visual models like fraction bars or circles, with at least 80% accuracy.
- Write equations to show how a fraction can be decomposed into unit fractions (e.g., 2/5 = 1/5 + 1/5).
- Explain, in their own words, why a fraction can be represented as the sum of its unit fractions.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Identify the vertex (h, k) and another point (x, y) on a parabola from a graph or description.
Distinguish between the vertex form equations for vertical and horizontal parabolas.
Substitute the coordinates of the vertex and a point into the appropriate vertex form equation.
Algebraically solve for the value of 'a', which determines the parabola's stretch and direction.
Write the final equation of a vertical parabola in the form y = a(x - h)^2 + k.
Write the final equation of a horizontal parabola in the form x = a(y - k)^2 + h.
Determine the direction a parabola opens based on its equation.
Ever wondered how a satellite dish perfectly focuses signals to one point, or the beautiful arc a basketball makes on its way to the hoop? 🏀 That pe...
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Key Concepts & Vocabulary
TermDefinitionExample
ParabolaA U-shaped curve where any point is at an equal distance from a fixed point (the focus) and a fixed line (the directrix).The path of a ball thrown into the air.
VertexThe highest, lowest, or furthest point on a parabola, representing its turning point. It is denoted by the coordinates (h, k).For a parabola that opens upwards, the vertex is the minimum point, like the bottom of a valley.
Axis of SymmetryA line that passes through the vertex and divides the parabola into two perfect mirror images.For a parabola with vertex (3, 4) that opens up or down, the axis of symmetry is the vertical line x = 3.
Vertex Form (Vertical)The standard equation for a parabola that opens upwards or downwards: y = a(x - h)^2 + k.The equation y = 2(x - 1)^2 + 5 represents a parabol...
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Core Formulas
Vertex Form for a Vertical Parabola
y = a(x - h)^2 + k
Use this form when the parabola opens up or down. (h, k) is the vertex. If a > 0, the parabola opens upwards. If a < 0, the parabola opens downwards.
Vertex Form for a Horizontal Parabola
x = a(y - k)^2 + h
Use this form when the parabola opens left or right. (h, k) is the vertex. If a > 0, the parabola opens to the right. If a < 0, the parabola opens to the left. Note that h is the x-coordinate and k is the y-coordinate of the vertex, but their positions in the formula are swapped compared to the vertical form.
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Challenging
Parabola P1 has a vertex at (2, 3) and passes through (4, 11). Parabola P2 has the same vertex (2, 3) but passes through (4, -5). If P1 has an equation with a value of a=a1 and P2 has a=a2, what is the relationship between a1 and a2?
A.a1 = -a2
B.a1 = a2
C.a1 = 2*a2
D.a1 = 1/a2
Challenging
A vertical parabola has an axis of symmetry at x = 1 and a maximum value of 8. If the parabola passes through the point (3, 0), what is its equation?
A.y = (x - 1)^2 + 8
B.y = -0.5(x - 1)^2 + 8
C.y = -2(x - 1)^2 + 8
D.y = 2(x + 1)^2 - 8
Challenging
A parabola passes through the points (-2, 7), (6, 7), and (2, -9). What is the equation of this parabola?
A.y = (x + 2)^2 - 9
B.y = 2(x - 6)^2 + 7
C.y = (x - 2)^2 - 9
D.y = -2(x + 2)^2 + 7
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What grade level is "Write equations of parabolas in vertex form using properties"?
Write equations of parabolas in vertex form using properties is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Write equations of parabolas in vertex form using properties?
You'll be able to: Identify the unit fractions that make up a given fraction (e.g., recognize that 3/4 is made up of 3 fractions of 1/4); Represent a fraction as the sum of unit fractions using visual models like fraction bars or circles, with at….
Is "Write equations of parabolas in vertex form using properties" free to practice?
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How many practice questions are included with Write equations of parabolas in vertex form using properties?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.