Write the equation for a parabola that has x− intercepts (−1.6,0) and (−3.2,0) and y−intercept (0,25.6).

Question

Please tell me what the equation is!!

Answer 1

Use the factored form:

 

y = a(x+1.6)(x+3.2)

 

To find the value of a, plug in (0,25.6):

 

25.6 = a(0+1.6)(0+3.2)

 

Solve for a. Once you have the value of a, multiply the factored form out to convert to standard form (y = ax²+bx+c).

Answer 2

vertex (-2.4, k)            halfway between -1.6 and -3.2

y = (x + 2.3)² + k        vertex form

0 = a(-1.6 + 2.3)² + k   

0 = a(-3.2 + 2.3)² + k

Solve for a

Substitute "a" and solve for k.

Answer 3

the graph passes through (-1.6,0) and (-3.2,0)

this means f(-1.6)=0 and f(-3.2)=0

therefore f(x)=(x+1.6)(x+3.2)

f(x)=x^2+4.8x+5.12

f(x)=k(x^2+4.8x+5.12) also passes through the above two points

f(x) passes through (0,25.6)

therefore 25.6=k(0^2+4.8*0+5.12)

25.6=k(5.12)

k=25.6/5.12

k=5

y=5(x^2+4.8x+5.12)

y=5x^2+24x+25.6