What type of curves does the equation y = a(x - h)^2 + k represent?

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Question: What type of curves does the equation y = a(x - h)^2 + k represent?

Options:

Correct Answer: Parabolas

Solution:

The equation y = a(x - h)^2 + k represents a family of parabolas with vertex at (h, k) and varying \'a\' determining the direction and width.

What type of curves does the equation y = a(x - h)^2 + k represent?

What type of curves does the equation y = a(x - h)^2 + k represent?

Step 1: Identify the equation format. The equation is in the form y = a(x - h)^2 + k.
Step 2: Recognize that this is a quadratic equation, which typically represents a parabola.
Step 3: Understand that 'a' affects the shape of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.
Step 4: Identify the vertex of the parabola. The vertex is the point (h, k). This is the highest or lowest point of the parabola depending on the value of 'a'.
Step 5: Note that changing 'a' will change how wide or narrow the parabola is. A larger absolute value of 'a' makes it narrower, while a smaller absolute value makes it wider.

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