Question

If graph of quadratic polynomial ax2 + bx +c is a downward parabola, then a is​

Answer 1

SOLUTION :

TO DETERMINE

$\sf{ If \: graph \: of \: quadratic \: polynomial \: \: y = a {x}^{2} + bx + c}$

is a downward parabola, then the value of a

EVALUATION

The given Quadratic polynomial is

$\sf{ y = a {x}^{2} + bx + c\: }$

We rewrite the above polynomial as below

$\displaystyle \sf{ \frac{y}{a} = {x}^{2} + \frac{b}{a} x + \frac{c}{a} \: }$

$\implies \displaystyle \sf{ \frac{y}{a} = { \bigg(x + \frac{b}{2a} \bigg )}^{2} + \frac{c}{a} - \frac{ {b}^{2} }{4 {a}^{2} } \: }$

$\implies \displaystyle \sf{ \frac{y}{a} + \frac{ {b}^{2} }{4 {a}^{2} } = { \bigg(x + \frac{b}{2a} \bigg )}^{2} + \frac{c}{a} \: }$

$\implies \displaystyle \sf{ \frac{y}{a} + \frac{ {b}^{2} }{4 {a}^{2} } - \frac{c}{a} = { \bigg(x + \frac{b}{2a} \bigg )}^{2} \: }$

$\implies \displaystyle \sf{ \frac{1}{a} \bigg( {y}+ \frac{ {b}^{2} }{4 {a}^{} } - c \bigg) = { \bigg(x + \frac{b}{2a} \bigg )}^{2} \: }$

Which is of standard form

$\sf{ {X}^{2} = 4AY\: }$

This shows that the quadratic polynomial represents a downward parabola when A < 0

Consequently the quadratic polynomial represents a downward

parabola when a < 0

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LEARN MORE FROM BRAINLY

The length of the latus rectum of the parabola

13[(x-3)^2+(y-4)^2 )= (2x-3y+ 5)^2

https://brainly.in/question/24980361

Answer 2

Answer:

If graph of quadratic polynomial a$x^{2}$ + bx +c is a downward parabola, then a

a<0

Step-by-step explanation: