A quadratic equation can be written in vertex form or standard form. Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task listed below and explain why.
A. factor the equation
b. graph the parabola
c. identify the vertex, minimum, or maximum of the parabola
d. solve the equation using quadratic formula
pls help I'm very lost
Well, to factor an equation you need to use the standard form. To graph the parabola, you need to use the vertex form. You also need the vertex form to identify the vertex, minimum, or maximum of the parabola. To solve the equation using the quadratic formula, you need to once again use the standard form.
The standard form is y = ax + bx + c
The quadratic formula is x = -b +- square root of b^2 -4ac, then you divide everything except x by 2a.
A quadratic equation can be factored from y = ax + bx + c. So the standard form can be used for both (a) and (d) (answer choices).
The form/equation above is used to identify the vertex and identify the maximum and minimum of a parabola.
I hope this helps you all!
Have a blessed day! 🙏🏽
Oh, oops. I forgot to say the vertex formula can be used for both (answer choices) (b) and (c).
Wow, I have the exact same question. If someone would answer this please, it would help over millions of people.
Sure! Let's go through each task one by one:
A. Factor the equation:
In this case, the standard form of the quadratic equation (ax^2 + bx + c = 0) would be more beneficial. This is because standard form allows you to easily see the coefficients (a, b, and c), which are needed to factor the equation. By factoring the equation, you can find its roots or zeros.
B. Graph the parabola:
For graphing the parabola, the vertex form of the quadratic equation (a(x-h)^2 + k) is more beneficial. This form directly provides the coordinates of the vertex (h, k). By knowing the vertex, you can easily plot it and determine the shape and position of the parabola.
C. Identify the vertex, minimum, or maximum of the parabola:
Again, the vertex form (a(x-h)^2 + k) is more helpful for identifying the vertex, minimum, or maximum of the parabola. The vertex is directly given by the values of (h, k) in this form. Additionally, the coefficient "a" can tell you whether the parabola opens upward (positive "a") or downward (negative "a"), which determines if it has a minimum or maximum point.
D. Solve the equation using the quadratic formula:
For solving the equation using the quadratic formula, the standard form (ax^2 + bx + c = 0) is the most suitable. The quadratic formula directly applies to equations in this form, allowing you to find the solutions easily. Plugging the values of a, b, and c into the formula will give you the roots of the equation.
Remember, both forms have their own advantages and their use depends on the specific task you are trying to accomplish with the quadratic equation.