Factored Form of Quadratics

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What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as y = a(x - p)(x - q), where p and q are the x-intercepts (or zeros) of the quadratic.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

To find the x-intercepts of a quadratic equation, set the equation equal to zero and solve for x.

Tags

CCSS.HSF-IF.C.7A

Front

What are the x-intercepts of the equation y = (x - 2)(x + 4)?

Back

The x-intercepts are 2 and -4.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean for a quadratic to have zeros at specific points?

Back

Having zeros at specific points means that the quadratic equation intersects the x-axis at those points.

Tags

CCSS.HSF-IF.C.7A

Front

If a quadratic has zeros at (1, 0) and (5, 0), what is its factored form?

Back

The factored form is y = (x - 1)(x - 5).

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the significance of the coefficient 'a' in the factored form of a quadratic?

Back

The coefficient 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine the vertex of a quadratic from its factored form?

Back

The vertex can be found by calculating the midpoint of the x-intercepts (p and q) and substituting it back into the equation to find the corresponding y-value.

Front

What is the relationship between the x-intercepts and the roots of a quadratic equation?

Back

The x-intercepts of a quadratic equation are the same as its roots, which are the values of x that make the equation equal to zero.

Tags

CCSS.HSF-IF.C.7A

Front

How do you convert a quadratic from standard form to factored form?

Back

To convert from standard form (ax^2 + bx + c) to factored form, you can use factoring techniques such as grouping or the quadratic formula to find the roots.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation in standard form.

Tags

CCSS.HSA-REI.B.4B