Graphing Quadratics & Solving

Front

What does it mean if the graph of a quadratic does not intercept the x-axis?

Back

It has No Real Solution.

Front

How can you determine if a quadratic equation has a maximum or minimum value?

Back

If the 'a' value is positive, it has a Minimum value; if 'a' is negative, it has a Maximum value.

Front

What are the zeros of the quadratic equation y = x² - 4?

Back

0 and 4.

Front

How many zeros does a parabola have if it touches the x-axis at one point?

Back

1 zero.

Front

What is the vertex of the quadratic equation y = 2(x - 2)² + 5?

Back

(2, 5).

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c.

Front

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

Back

It determines the direction of the parabola (upward if positive, downward if negative).

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

How do you find the y-intercept of a quadratic equation?

Back

Set x = 0 and solve for y.

Front

What is the significance of the discriminant in a quadratic equation?

Back

It determines the number and type of solutions: positive (2 real solutions), zero (1 real solution), negative (no real solutions).