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Questions and Answers
Which form of a parabola's equation can be written as $y = a(x - h)^2 + k$?
Which form of a parabola's equation can be written as $y = a(x - h)^2 + k$?
- Standard form
- Vertex form (correct)
- Intercept form
- General form
What does the value of $a$ represent in the vertex form of a parabola's equation?
What does the value of $a$ represent in the vertex form of a parabola's equation?
- The x-coordinate of the vertex
- The y-coordinate of the vertex
- The axis of symmetry
- The coefficient of the quadratic term (correct)
How can we find the equation of a parabola using the vertex form?
How can we find the equation of a parabola using the vertex form?
- By finding the coordinates of the vertex and substituting them into the equation (correct)
- By finding the y-intercept and substituting it into the equation
- By finding the x-intercepts and substituting them into the equation
- By finding the axis of symmetry and substituting it into the equation
What is the vertex of a parabola?
What is the vertex of a parabola?
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What is the purpose of rewriting a parabola's equation in vertex form?
What is the purpose of rewriting a parabola's equation in vertex form?
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Study Notes
Vertex Form of a Parabola's Equation
- The vertex form of a parabola's equation can be written as y = a(x - h)^2 + k.
Representation of 'a' in Vertex Form
- The value of 'a' represents the vertical stretch factor, telling us how skinny or fat the parabola is.
Finding a Parabola's Equation Using Vertex Form
- To find the equation of a parabola using the vertex form, we need to know the vertex (h, k) and the value of 'a'.
Vertex of a Parabola
- The vertex of a parabola is the lowest or highest point on the graph, represented by (h, k), where 'h' is the x-coordinate and 'k' is the y-coordinate.
Purpose of Rewriting a Parabola's Equation in Vertex Form
- The purpose of rewriting a parabola's equation in vertex form is to easily identify the vertex, axis of symmetry, and direction of opening, making it easier to graph the parabola.
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