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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSA-REI.B.4B

Front

What is the quadratic formula?

Back

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

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B