Quadratic Roots

Front

What is a quadratic equation?

Back

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

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that satisfy the equation, meaning they make the equation equal to zero.

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 quadratic to have no real solutions?

Back

A quadratic has no real solutions when the discriminant (b² - 4ac) is less than zero, indicating that the graph does not intersect the x-axis.

Tags

CCSS.HSA-REI.B.4B

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of a function crosses the x-axis, corresponding to the roots of the equation.

Tags

CCSS.HSF-IF.C.7D

Front

How can you find the roots of a quadratic graphically?

Back

You can find the roots of a quadratic graphically by identifying the points where the parabola intersects the x-axis.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

What is the significance of the discriminant?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What are the zeroes of a function?

Back

The zeroes of a function are the values of x for which the function equals zero, synonymous with the roots of the equation.

Tags

CCSS.HSF-IF.C.7D