What is the quadratic formula?
Algebra 2: Mid Year Assessment

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Mathematics
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11th Grade
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Hard
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1.
FLASHCARD QUESTION
Front
Back
The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).
2.
FLASHCARD QUESTION
Front
How do you simplify the expression (2 + 4i)(3 + 5i)?
Back
To simplify, use the distributive property: (2)(3) + (2)(5i) + (4i)(3) + (4i)(5i) = 6 + 10i + 12i + 20i². Since i² = -1, this becomes 6 + 22i - 20 = -14 + 22i.
3.
FLASHCARD QUESTION
Front
What is the process to solve the equation 2x² - 5x = 1?
Back
First, rearrange the equation to standard form: 2x² - 5x - 1 = 0. Then apply the quadratic formula: x = (5 ± √(25 + 8)) / 4.
4.
FLASHCARD QUESTION
Front
What does it mean for a function to be quadratic?
Back
A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a ≠ 0.
5.
FLASHCARD QUESTION
Front
What is the vertex of a parabola given by the equation y = ax² + bx + c?
Back
The vertex can be found using the formula (-b/(2a), f(-b/(2a))).
6.
FLASHCARD QUESTION
Front
How do you determine the axis of symmetry for a quadratic function?
Back
The axis of symmetry for a quadratic function in the form y = ax² + bx + c is given by the line x = -b/(2a).
7.
FLASHCARD QUESTION
Front
What is the discriminant in a quadratic equation, and what does it indicate?
Back
The discriminant is the part of the quadratic formula under the square root, b² - 4ac. It indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.
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