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

A sphere has a radius of 7 cm. What is its volume?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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What is the probability of drawing an ace from a standard deck of 52 cards?

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What is the sum of the first 10 positive even numbers?

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

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