If y=a x2+b x+c represents a parabola with vertex A as shown in the figure and b2=2(b+2 a c), where a ≠ 0 and AP =3, then OP equals ( O is origin)

Question

If y=a x2+b x+c represents a parabola with vertex A as shown in the figure and b2=2(b+2 a c), where a ≠ 0 and AP =3, then OP equals ( O is origin) (A) 3 (B) 6 (C) (3/4) (D) (3/2)

Tardigrade Admin · Accepted Answer

b 2=2 b +4 ac ⇒ 4 ac - b 2=-2 b ⇒ AP = OP =3

Q. If $y = a x^{2} + b x + c$ represents a parabola with vertex $A$ as shown in the figure and $b^{2} = 2 (b + 2 a c)$ , where $a \neq = 0$ and $A P = 3$ , then $OP$ equals ( $O$ is origin)

3

6

$\frac{3}{4}$

$\frac{3}{2}$

$b^{2} = 2 b + 4 a c \Rightarrow 4 a c - b^{2} = - 2 b$
$\Rightarrow A P = OP = 3$

Q. If y=ax2+bx+c represents a parabola with vertex A as shown in the figure and b2=2(b+2ac), where a=0 and AP=3, then OP equals ( O is origin)

3

6

43​

23​

b2=2b+4ac⇒4ac−b2=−2b ⇒AP=OP=3

Q. If $y = a x^{2} + b x + c$ represents a parabola with vertex $A$ as shown in the figure and $b^{2} = 2 (b + 2 a c)$ , where $a \neq = 0$ and $A P = 3$ , then $OP$ equals ( $O$ is origin)

$\frac{3}{4}$

$\frac{3}{2}$

$b^{2} = 2 b + 4 a c \Rightarrow 4 a c - b^{2} = - 2 b$
$\Rightarrow A P = OP = 3$