Unit 4 Quadratics Review....so far

Front

What is the vertex of a parabola given by the equation f(x) = ax^2 + bx + c?

Back

The vertex of the parabola can be found using the formula: \( \left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right) \).

Front

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

Back

To find the y-intercept of a quadratic function, set x = 0 and solve for y.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which f(x) = 0. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as \( a(x - r_1)(x - r_2) \), where r_1 and r_2 are the roots of the equation.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola opens upwards if the coefficient of x^2 (a) is positive and downwards if a is negative.

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.

Front

What is the axis of symmetry of a parabola?

Back

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

Front

How do you complete the square for a quadratic equation?

Back

To complete the square, rearrange the equation to isolate the x terms, then add and subtract the square of half the coefficient of x.

Front

What is the quadratic formula?

Back

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

Front

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

Back

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