Question

Which of the following is in standard form of quadratic?

ƒ(x) = −5x² – 3x +9
ƒ(x) = −5(x + 4)(x − 2)
f(x)=2x-8
f(x) = -5(x - 1)² + 6

Answer 1

f(x) = -5x² - 3x +9

Explanation:

The standard form of a quadratic function is: f(x) = ax² + bx + c

The intercept form of a quadratic function is: f(x) = a(x - p)(x - q)

The vertex form of a quadratic function is: f(x) = a(x - h)² + k

(when a ≠ 0)

Therefore:

f(x) = -5x² - 3x +9

• This is in standard form of a quadratic equation.

f(x) = -5(x + 4)(x - 2)

• This is in intercept form of a quadratic equation.
• The x-intercepts are x = -4 and x = 2.

f(x) = 2x - 8

• This is a linear equation as the greatest exponent of the variable is 1.

f(x) = -5(x - 1)² + 6

• This is in vertex form of a quadratic equation.
• The vertex is (1, 6).

Answer 2

first option

Explanation:

the standard form of a quadratic function is

f(x) = ax² + bx + c ( a ≠ 0 )

the only function in this form from the list is

f(x) = - 5x² - 3x + 9