Graphing Quadratics & Solving

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic equation look like?

Back

The graph of a quadratic equation is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the vertex's x-coordinate.

Front

What are the zeros of a quadratic function?

Back

The zeros (or roots) of a quadratic function are the x-values where the graph intersects the x-axis, meaning where y = 0.

Front

How can you find the zeros of a quadratic equation?

Back

You can find the zeros by factoring the equation, using the quadratic formula, or by completing the square.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards when the coefficient 'a' in the quadratic equation is positive, indicating that the vertex is the minimum point.

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What does it mean for a parabola to open downwards?

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A parabola opens downwards when the coefficient 'a' in the quadratic equation is negative, indicating that the vertex is the maximum point.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

How do you determine the number of zeros a quadratic function has?

Back

The number of zeros can be determined by the discriminant (b² - 4ac): if it's positive, there are 2 zeros; if zero, 1 zero; if negative, no real zeros.