Quadratic Features

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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

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 does the axis of symmetry represent in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form.

Tags

CCSS.HSF-IF.C.7A

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts, also known as roots or zeros, are the points where the graph intersects the x-axis, found by solving the equation f(x) = 0.

Tags

CCSS.HSF-IF.C.7A

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, depending on the direction it opens.

Front

How can you determine if the vertex is a maximum or minimum?

Back

If the parabola opens upwards, the vertex is a minimum; if it opens downwards, the vertex is a maximum.

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