Topic Details (Notes format)

How to Graph Quadratic Functions (Vertex Form)

Subject: Mathematics

Book: Maths Mastery

A quadratic in vertex form is y = a(x–h)² + k, where (h, k) is the vertex. This format makes identifying vertex location, axis of symmetry (x=h), and direction (a>0 opens up, a<0 opens down) straightforward. For instance, y=2(x–1)²–4 has vertex at (1, –4). Vertex form aids in quick graphing, transformations, and completing the square. You can easily find maxima/minima or intervals of increase/decrease. This approach extends to analyzing parabolas in physics, optimizing business problems, or constructing geometric shapes requiring symmetrical curves.

Practice Questions

If x:y = 2:3 and z:y = 4:3, what is x:z?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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If 2a + b = 10 and a - b = 4, what is the value of a?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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