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 its orientation. It can be found using the formula \( x = -\frac{b}{2a} \) for a quadratic equation in the form \( ax^2 + bx + c \).

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Tags

CCSS.HSA-REI.B.4B

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions (roots) of a quadratic equation of the form \( ax^2 + bx + c = 0 \) and is given by \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant, given by \( b^2 - 4ac \), indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve a quadratic equation by completing the square?

Back

To solve by completing the square, rearrange the equation to isolate the constant, then add the square of half the coefficient of \( x \) to both sides, and factor the left side.

Tags

CCSS.HSA-REI.B.4B

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is \( ax^2 + bx + c = 0 \), where \( a \), \( b \), and \( c \) are constants and \( a \neq 0 \).

Front

How do you solve \( (x + 11)^2 = 36 \)?

Back

To solve, take the square root of both sides: \( x + 11 = \pm 6 \). This gives two equations: \( x + 11 = 6 \) and \( x + 11 = -6 \), leading to \( x = -5 \) or \( x = -17 \).

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry of a parabola given by the equation \( y = ax^2 + bx + c \) is found using the formula \( x = -\frac{b}{2a} \).

Front

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

Back

The leading coefficient (the coefficient of \( x^2 \)) determines the direction of the parabola: if positive, it opens upwards; if negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A