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

The LCM of 12 and 15 is:

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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What is the HCF of 48 and 180?

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What is the value of x if log(x) + log(4) = log(32)?

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What is the value of x if 3x + 7 = 16?

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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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What is the HCF of 72 and 120?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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What is the slope of a line passing through the points (2, 3) and (4, 7)?

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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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