Solving Quadratics by graphing

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean for a function to have zeros?

Back

Zeros of a function are the values of x for which the function's output is zero. They are the x-intercepts of the graph.

Tags

CCSS.HSF-IF.C.7D

Front

How can you find the zeros of a quadratic function graphically?

Back

You can find the zeros of a quadratic function by identifying the points where the graph intersects the x-axis.

Tags

CCSS.HSF-IF.C.7A

Front

What are x-intercepts?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What is the vertex of a quadratic function?

Back

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

Front

What is the difference between maximum and minimum in a quadratic function?

Back

A maximum is the highest point on the graph of a quadratic function (when it opens downwards), while a minimum is the lowest point (when it opens upwards).

Tags

CCSS.HSF-IF.C.7A

Front

How many solutions can a quadratic equation have?

Back

A quadratic equation can have two solutions, one solution, or no real solutions, depending on the discriminant (b² - 4ac).

Tags

CCSS.HSA-REI.B.4B

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature and number of solutions.

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CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real solution (a repeated root).

Tags

CCSS.HSA-REI.B.4B