Question

Find the y-intercept for the parabola defined by
this equation:
y=-4x^2-x+3

Answer 1

(0,3)

Explanation:

Two methods:

Method 1: General method for any equation

Method 2: Method specific for parabolas in standard form

Method 1: General method for any equation

For any two-variable equation to be graphed, the y-intercept is the point where the graph crosses the y-axis. The y-axis is a vertical line through the origin (0,0).

Any y-intercept is on that line, and to get to that point starting from the origin, one can't travel left or right to get to the y-intercept point (without moving back to the y-axis). The only movement would be up or down.

Since no left-right movement will happen, the x-coordinate is zero.

For any two-variable equation, the x and y coordinates of any point on the graph are linked by the equation. If it is known that the x-value is zero, the y-value associated with that x-value is given by substituting zero into the equation everywhere there is an "x", and solving for "y".

`y=-4x^2-x+3`

`y=-4(0)^2-(0)+3`

Order of operations requires exponents before multiplication, or addition & subtraction...

`y=-4(0)-(0)+3`

multiplication...

`y=0-0+3`

addition & subtraction, from left to right...

`y=3`

So, when the x-value is zero, the y-value is three. Therefore, the ordered pair representing that point is (0,3).

Method 2: Method specific for parabolas in standard form

The given equation is the equation for a parabola (as stated in the question), and it is given in "standard form":
`y=ax^2+bx+c`, where a, b, and c are real numbers (and a isn't equal to zero, because then the x-squared term would be zero, and the equation would really just be a linear equation).

Note that for our equation, it is in standard form if we rewrite the equation to only use addition,
`y=-4x^2+-1x+3`, where
`a=-4, ~b=-1 ~ \text{and}~c=3`

For a parabola in standard form, the y-intercept is always at a height of "c".

So, the y-intercept would be (0,3).

Answer 2

y is 0,3

Step-by-step explanation:

To find the x-intercept, substitute in

0

for

y

and solve for

x

. To find the y-intercept, substitute in

0

for

x