Question

Can u guys please answer this question. this is extremely urgent

A parabola with equation of the form
y = ax2 + c has its vertex at (0, −7) and
passes through (4, 1). Find values for a, c
and hence find the equation of the
parabola

Answer 1

Step-by-step explanation:

$y = a {x}^{2} + c$

at (0,,-7)

$x = 0 \: y = - 7$

that is

$- 7 = a {0}^{2} + c \\ c = - 7$

at (4,1)

$x = 4 \: \: \: \: y = 1$

$1 = a {4}^{2} + ( - 7) \\ 1 = 16a - 7 \\ 16a = 8 \\ a = \frac{1}{2}$

Hence equation of the parabola is

$y = \frac{1}{2} {x}^{2} - 7$