IXL Algebra 2 N.4 answer key
The Correct Answer and Explanation is :
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Understanding Quadratic Functions
In Algebra 2, one of the key topics is quadratic functions, which are polynomial functions of degree two. The standard form of a quadratic function is:
[
f(x) = ax^2 + bx + c
]
where ( a ), ( b ), and ( c ) are constants. The shape of the graph of a quadratic function is a parabola, which opens upwards if ( a > 0 ) and downwards if ( a < 0 ).
Vertex and Axis of Symmetry
The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens. The x-coordinate of the vertex can be found using the formula:
[
x = -\frac{b}{2a}
]
The line ( x = -\frac{b}{2a} ) is also known as the axis of symmetry, which divides the parabola into two mirror-image halves.
Finding Roots
The roots (or zeros) of the quadratic function, where ( f(x) = 0 ), can be found using factoring, completing the square, or the quadratic formula:
[
x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}
]
The discriminant ( b^2 – 4ac ) determines the nature of the roots:
- If it’s positive, there are two distinct real roots.
- If it’s zero, there is one real root (a repeated root).
- If it’s negative, there are no real roots (the solutions are complex).
Graphing Quadratics
When graphing, it’s important to identify the vertex, axis of symmetry, and roots. Plotting these points and using the symmetry of the parabola allows for a more accurate representation of the function.
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