Math 1 Quadratics Review for EOC

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x that make the function equal to zero. They are the points where the graph intersects the x-axis.

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

The vertex of a parabola in standard form y = ax² + bx + c can be found using the formula x = -b/(2a). Substitute this x-value back into the equation to find the y-coordinate.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression of the form ax² + bx + c, find two numbers that multiply to ac and add to b. Rewrite the expression using these numbers and factor by grouping.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you determine the axis of symmetry for a parabola?

Back

The axis of symmetry for a parabola given by the equation y = ax² + bx + c is the vertical line x = -b/(2a).

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex. If a > 0, the parabola opens upwards and has a minimum value; if a < 0, it opens downwards and has a maximum value.

Front

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

Back

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

Front

What is the relationship between the roots and the coefficients of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.