Unit 5 Retest - Algebra
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Mathematics
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10th Grade
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Medium
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1.
FLASHCARD QUESTION
Front
What is the vertex of a quadratic function in standard form?
Back
The vertex of a quadratic function in standard form, f(x) = ax^2 + bx + c, can be found using the formula: \( \left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right) \).
2.
FLASHCARD QUESTION
Front
How do you find the coordinates of the vertex for the function f(x) = x^2 - 12x + 8?
Back
The vertex can be found using the formula: \( x = -\frac{b}{2a} \). Here, a = 1 and b = -12, so x = 6. Plugging x back into the function gives f(6) = -28, so the vertex is (6, -28).
3.
FLASHCARD QUESTION
Front
What is the discriminant in the quadratic formula?
Back
The discriminant is given by the formula: \( D = b^2 - 4ac \). It determines the nature of the roots of the quadratic equation.
4.
FLASHCARD QUESTION
Front
What does a negative discriminant indicate about the roots of a quadratic equation?
Back
A negative discriminant indicates that the quadratic equation has two complex (imaginary) roots.
5.
FLASHCARD QUESTION
Front
What is the next step to solve the equation x^2 + 6x + 9 = -17 using complex numbers?
Back
The next step is to factor the left side to (x + 3)^2, which simplifies the equation.
6.
FLASHCARD QUESTION
Front
What is the vertex form of a quadratic function?
Back
The vertex form of a quadratic function is given by: \( f(x) = a(x - h)^2 + k \), where (h, k) is the vertex.
7.
FLASHCARD QUESTION
Front
How do you convert a quadratic function from standard form to vertex form?
Back
To convert from standard form to vertex form, complete the square on the quadratic expression.
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