Roots of Quadratics

Front

What are the x-intercepts of the quadratic function y = x² - 3x - 10?

Back

The x-intercepts are x = 5 and x = -2.

Tags

CCSS.HSF-IF.C.7A

Front

How many solutions (roots) does the graph of the function y = x² - 3x - 10 have?

Back

The graph has no solutions.

Front

What are the zeros of the quadratic function y = x² - 2x - 15?

Back

The zeros (roots) are x = -3 and x = 5.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the range of the function y = x² - 3x - 10?

Back

The range is [-2, +∞).

Front

What are the roots of the function f(x) = (x - 2)(x + 3)?

Back

The roots are x = 2 and x = -3.

Tags

CCSS.HSF-IF.C.7C

Front

Define a quadratic function.

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: D > 0 means two real roots, D = 0 means one real root, and D < 0 means no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the function to find y.

Front

What is the vertex of the function y = x² - 4x + 3?

Back

The vertex is at (2, -1).