Graphing Quadratics & Solving

Front

What is the line of symmetry for a parabola?

Back

The line of symmetry for a parabola is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a) for a quadratic equation in the form y = ax^2 + bx + c.

Front

How do you determine the number of zeros (roots) of a parabola?

Back

The number of zeros of a parabola can be determined by calculating the discriminant (D = b^2 - 4ac) of the quadratic equation. If D > 0, there are 2 zeros; D = 0 means 1 zero; D < 0 indicates no real zeros.

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. It can be found using the formula (-b/(2a), f(-b/(2a))) for a quadratic equation in the form y = ax^2 + bx + c.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find the x-intercepts of a parabola?

Back

To find the x-intercepts of a parabola, set y = 0 in the quadratic equation and solve for x. This can be done using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean for a parabola to open upwards or downwards?

Back

A parabola opens upwards if the coefficient 'a' in the equation y = ax^2 + bx + c is positive, and it opens downwards if 'a' is negative.

Front

What is the axis of symmetry for the parabola y = 2x^2 + 4x + 1?

Back

The axis of symmetry can be found using x = -b/(2a). For this equation, it is x = -4/(2*2) = -1.

Front

How do you complete the square for the quadratic equation y = x^2 - 6x + 11?

Back

To complete the square, rewrite the equation as y = (x - 3)^2 + 2, which shows the vertex at (3, 2).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, indicating the highest or lowest value of the function.