What is the vertex form of a quadratic function?
Unit 3 STUDY GUIDE

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Mathematics
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12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
The vertex form of a quadratic function is given by the equation: y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
2.
FLASHCARD QUESTION
Front
What does the coefficient 'a' in the quadratic function y = ax² + bx + c determine?
Back
The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).
3.
FLASHCARD QUESTION
Front
How do you find the maximum or minimum value of a quadratic function?
Back
The maximum or minimum value of a quadratic function can be found at the vertex, which occurs at x = -b/(2a). If 'a' is positive, it is a minimum; if 'a' is negative, it is a maximum.
4.
FLASHCARD QUESTION
Front
What is the quadratic formula?
Back
The quadratic formula is used to find the roots of a quadratic equation and is given by: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
5.
FLASHCARD QUESTION
Front
What is the discriminant in a quadratic equation?
Back
The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.
6.
FLASHCARD QUESTION
Front
How do you convert a quadratic equation from standard form to vertex form?
Back
To convert from standard form (y = ax² + bx + c) to vertex form (y = a(x - h)² + k), complete the square.
7.
FLASHCARD QUESTION
Front
What is the axis of symmetry in a quadratic function?
Back
The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves and is given by the equation x = -b/(2a).
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