find the x-intercepts of the parabola with vertex (4,-1) and y-intercept (0,15) write your answer in this form:(x1,y1),(x2,y2) f necessary, round to the nearest Hundredth

Question

campbell_st · Answer

well the vertex form of a parabola is 

$$y=a(x - h)^2 + k$$

where (h, k) is the vertex. 

so substitute you vertex values, h = 4 and k = -1 

into the equation. 

tThe y-intercept is on the parabola... so to find the value of a you need to substitute 

x = 0 and y = 15  and solve for a. 

then you can rewrite the equation of the parabola in standard form

that's the 1st part

hope it makes sense

campbell_st · Answer

once you have the equation in standard form you may need to use the general quadratic formula for the x intercepts

anonymous · Answer

soo would it be y=x^2-8x+15

campbell_st · Answer

that's the correct equation...

and the equation can be factored.

anonymous · Answer

its wrong

campbell_st · Answer

so what did you get for the x-intercepts

anonymous · Answer

-4

campbell_st · Answer

the equation is 

$$y=x^2 - 8x + 15~~~~then~~~~y=(x -5)(x-3)$$

campbell_st · Answer

so the intercepts are

campbell_st · Answer

where y = 0

so solve 

x - 5 = 0     and x - 3 = 0

anonymous · Answer

am confused

campbell_st · Answer

ok.... so the x-intercepts these are points on the x-axis so y = 0

if you have a parabola to find the x-intercepts let y = 0 and solve for x

so 

$$0 = x^2 - 8x + 15~~~or~~~0 =(x -5)(x -3)$$

if either of the factors (x -5) or (x -3) are equal to zero the equation is equal to zero... 

so then you need to let the factors equal  zero and solve for x


so solve 

x - 5 = 0    and x - 3 = 0    what would you have...?

campbell_st · Answer

the other thing to think about is that the x-intercepts are the same distance from the x value in the vertex .

anonymous · Answer

am go fail this test

campbell_st · Answer

so if you the solve the 2 equations what do you get

x - 5 = 0   and x - 3 = 0

campbell_st · Answer

these values are the x-intercepts

anonymous · Answer

x=5,3

campbell_st · Answer

correct so the intercepts are at (3,0) and (5, 0)

the vertex has an x value of x = 4... the intercepts are the same distance from this value

anonymous · Answer

thank u soo much

campbell_st · Answer

yw

anonymous · Answer

it was wrong

campbell_st · Answer

so did you write the intercepts as (3, 0) and (5, 0)..?

anonymous · Answer

yea

campbell_st · Answer

here is a graph of the parabola you gave... and it meets all the conditions...

can you check the vertex is (4, -1) and y-intercept is y = 15  or (0. 15)