Quadratics Part 1

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula \( x = -\frac{b}{2a} \) for the quadratic equation \( ax^2 + bx + c \).

Front

How do you identify the coefficients a, b, and c in a quadratic equation?

Back

In the standard form of a quadratic equation \( ax^2 + bx + c = 0 \), 'a' is the coefficient of \( x^2 \), 'b' is the coefficient of \( x \), and 'c' is the constant term.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a' in the equation \( ax^2 + bx + c \).

Front

How do you find the vertex of the parabola given in vertex form?

Back

In vertex form \( y = a(x-h)^2 + k \), the vertex is the point \( (h, k) \).

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if 'a' > 0, downward if 'a' < 0) and affects the width of the parabola.

Front

What transformation occurs when you change the equation from \( f(x) = x^2 \) to \( g(x) = (x + 4)^2 \)?

Back

This represents a horizontal translation of the graph 4 units to the left.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

You can complete the square to rewrite the equation in the form \( y = a(x-h)^2 + k \).

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 \( x = -\frac{b}{2a} \).

Front

How do you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex. If 'a' is positive, the vertex is a minimum; if 'a' is negative, the vertex is a maximum.

Front

What is the quadratic formula used for?

Back

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