Question

4. What is the standard form of the equation

Answer 1

A quadratic function is a polynomial of the form f(x) = a·x² + b·x + c, where a, and b are coefficients and c, a constant, are numbers, a is a non zero number

The correct options are;

4. c. -3·x² + 2·x + 9 = 0

5. d. -9 and 7

6. b. 4·x² - 25 = 0

7. c. Real irrational and not equal

8. c. m² + 4·m + 13 = 0

9. a. y = x² - 4·x - 21

10. c. Parabola

The reasons why the above options are selected are given as follows:

4. The given equation, x·(2 - 3·x) + 9 = 0, can be rewritten as follows;

x·(2 - 3·x) + 9 = 2·x - 3·x² + 9 = -3·x² + 2·x + 9 = 0

Therefore, correct option is c. -3·x² + 2·x + 9 = 0

5. The given quadratic equation, x² + 2·x - 63 = 0, can be factorized as follows;

Given that he coefficient f x² is 1, and  9 × (-7) = -63, and 9 - 7 = 2, we have;

x² + 2·x - 63 = (x + 9)·(x - 7) = 0

The roots of the equation are -9, and 7

The correct option is option d. -9 and 7

6. The equation that can be easily solved by extracting the square root is the equation that is separable into squares of the constant and square of the required variable

4·x² = 25

$x = \sqrt{\dfrac{25}{4} } = \dfrac{5}{2}$

The correct option is b. 4·x² - 25 = 0

7. A quadratic equation that has a discriminant of 20, gives values of x in the forms;

$x = \dfrac{-b \pm \sqrt{20} }{2\cdot a}$

Given that √20 = 2·√5, is an irrational number, we have that the results are real irrational and not equal

The correct option is option c. Real irrational and not equal

8. The given equation is (m + 2)² + 9 = 0

(m + 2)² + 9 = m² + 4·m + 4 + 9 = m² + 4·m + 13 = 0

The correct option is c. m² + 4·m + 13 = 0

9. A quadratic function is a function given in the form f(x) = a·x² + b·x + c

Where, f(x) = y, the correct option is option a.

a. y = x² - 4·x - 21

10. The shape of a quadratic function is the shape of a parabola

The correct option is option c.

c. Parabola

Learn more about quadratic functions here:

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