Graphing Quadratic Ch 7

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent?

Back

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

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set y = 0 and solve the equation ax² + bx + c = 0.

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 formula x = -b/(2a).

Front

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

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 is the intercept form of a quadratic function?

Back

The intercept form is written as y = a(x - p)(x - q), where p and q are the x-intercepts.

Front

How do you determine the number of solutions (x-intercepts) a quadratic has?

Back

The number of solutions can be determined using the discriminant (b² - 4ac): if > 0, two solutions; = 0, one solution; < 0, no solutions.

Front

What transformation occurs in the function y = a(x - h)² + k?

Back

This represents a vertical stretch/shrink by a factor of |a|, and a translation of h units right (if h > 0) or left (if h < 0) and k units up (if k > 0) or down (if k < 0).

Front

What is the formula to find the vertex of a quadratic in standard form?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What does it mean if a quadratic function has no real solutions?

Back

It means the graph of the quadratic does not intersect the x-axis, indicating that the discriminant is negative.