determine a quadratic funtion with the given information; y-intercept of -4 and vertex (3,-7)

Question

ash2326 · Answer

A quadratic function or a parabola.
Have you studied parabolas?

eyust707 · Answer

Well a quadratic function is of the form:
$$ax^2 + bx +c$$

eyust707 · Answer

The y-intercept occurs when x is 0. Which means c must equal -4.

eyust707 · Answer

The x coordinate of the vertex of a parabola is -b/2a. So:
$$3={-b \over 2a}$$
$$6a=-b$$
$$-6a =b$$
And the y coordinate is -7, So when we plug in a 3 we better get -7
$$f(3)= -7 = a(3)^2+b(3)-4 $$
$$-7=a9+b3-4$$
$$-3=9a+3b$$
but before we said b must be -6a
$$-3=9a+3(-6a)$$
$$-3=9a-18a)$$
$$-3=-9a$$
$$a=1/3$$
Then plug a back in to get b
$$-6a =b$$
$$-6({1 \over 3}) = b$$ 
$$b=-2$$

$${1\over3}x^2 -2x -4$$

anonymous · Answer

thank you !!