Solving and graphing quadratics flashcardziz assessment

Front

What is a quadratic function?

Back

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

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form y = ax^2 + bx + c can be found using the formula (-b/(2a), f(-b/(2a))).

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 equation x = -b/(2a).

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing on an interval if the output values rise as the input values increase, and decreasing if the output values fall as the input values increase.

Front

How do you determine the intervals of increase and decrease for a quadratic function?

Back

To determine the intervals of increase and decrease, find the vertex and analyze the sign of the leading coefficient (a). If a > 0, the function decreases to the left of the vertex and increases to the right; if a < 0, it increases to the left and decreases to the right.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation to zero and solving for x using factoring, completing the square, or the quadratic formula.

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.

Front

What is the significance of the discriminant in a quadratic equation?

Back

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