In the cloud storage below, write your answer in paragraph for the following questions.
Answers
Answer:
1) when do you think is it necessary to express a quadratic function in the form of y = ax^2 +b + c?
(2) when is it necessary to express it in vertex form?
(3) which solution do you find easier in transforming a quadratic function ( completing the square or using h and k values) and state the reason (s) why?
The answer to the given question is as follows:
1). When do you think is it necessary to express a quadratic function in the form of y = ax² + bx + c?
Ans: It is necessary to express a quadratic function in the form of y = ax² + bx + c when "a" is positive, the parabola opens upward and the vertex is the minimum value.
2). When is it necessary to express it in vertex form?
Ans: Vertex form is used when you have to form the graph of the given equation. Because it is easy to plot it on the graph in vertex form.
3). Which solution do you find easier in transforming a quadratic function (completing the square or using h and k values) and state the reason (s) why?
Ans: It is easier to convert the quadratic equation in the form of y = ax² + bx + c because there are many formulas applicable in this form.
4). Give one quadratic function written in the form of y = ax² + bx + c and transform it to its vertex form. Then, transform the vertex form back to its form y = ax² + bx + c. Show your solution for the whole process.
Ans: Step 1: To convert a general (standard) form of a quadratic equation a x 2 + b x + c = 0 to the vertex form a ( x − h ) 2 + k = 0 , find h, the x-coordinate of the vertex, by computing h = − b 2 a .
Step 2: Find k, the y-coordinate of the vertex, by substituting the x-coordinate of the vertex, h, into the equation k = a h 2 + b h + c .
Step 3: Complete the vertex form of the equation by substituting h and k found in steps 1 and 2 into a ( x − h ) 2 + k = 0 form.