Algebra 2 Quadratics Test

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Questions and Answers

What is the vertex form of a quadratic function?

y = a(x + h)^2 - k
y = a(x - h)^2 + k (correct)
y = ax^2 + bx + c
y = x^2 + px + q

What does the discriminant of a quadratic equation determine?

The vertex of the parabola
The sum of the roots of the equation
The product of the roots of the equation
The number and type of roots the equation has (correct)

What is the axis of symmetry of a parabola given by the equation y = 3x^2 - 6x + 2?

x = -1
x = -3
x = 3
x = 1 (correct)

Study Notes

Quadratic Functions

The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Discriminant of a Quadratic Equation

The discriminant of a quadratic equation ax^2 + bx + c = 0 is b^2 - 4ac.
It determines the nature of the roots of the equation:
- If b^2 - 4ac > 0, the equation has two distinct real roots.
- If b^2 - 4ac = 0, the equation has one repeated real root.
- If b^2 - 4ac < 0, the equation has no real roots.

Axis of Symmetry

The axis of symmetry of a parabola given by the equation y = 3x^2 - 6x + 2 is x = -b / 2a, which is x = (-(-6)) / (2 * 3) = 1.

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Description

Test your understanding of quadratics in Algebra 2 with this quiz. Explore topics such as quadratic equations, vertex form, and solving quadratic functions.