Graphing Quadratic Equations

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c

Front

What is the vertex of the parabola represented by the equation y = x² + 16x + 71?

Back

V(-8, 7)

Front

How many zeros can a quadratic equation have?

Back

A quadratic equation can have 0, 1, or 2 zeros.

Front

What is the axis of symmetry in a quadratic equation?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror images, given by the formula x = -b/(2a).

Front

When does a parabola have a minimum value?

Back

A parabola has a minimum value when the coefficient 'a' in the standard form is positive.

Front

What does the coefficient 'a' determine in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola (upward if positive, downward if negative) and the width of the parabola.

Front

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

Back

The vertex represents the highest or lowest point of the parabola, depending on the direction it opens.

Front

How can you find the zeros of a quadratic equation?

Back

You can find the zeros by factoring, using the quadratic formula, or by completing the square.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant (b² - 4ac) tell you about a quadratic equation?

Back

The discriminant indicates the number of real solutions: if positive, there are 2 solutions; if zero, there is 1 solution; if negative, there are no real solutions.