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'.

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CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7C

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean for a parabola to open downwards?

Back

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

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSA-REI.B.4B