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 = 4:5 and y:z = 2:3, what is x:z?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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If 3x = 81, what is the value of x?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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

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A car travels 240 km in 4 hours. What is its average speed?

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If a number is divisible by 9, it is also divisible by which of the following?

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What is the square root of 0.25?

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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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If a:b = 3:4 and b:c = 5:6, what is a:c?

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