Question

Besties this is 100 points & i'll give brainliest istg i need to know this

Answer 1

Answer:

$\displaystyle b = - 14$

$\displaystyle c = - 54$

Step-by-step explanation:

to figure out b we can consider the following formula:

$\displaystyle \frac{ - b}{2a} = h$

the form of vertex coordinate given by

$\displaystyle (h,k)$

so according to the question

$\displaystyle (h,k) = ( - 7, - 5)$

by order pair we obtain:

$\displaystyle h = - 7, k = - 5$

now substitute the value of h and a to the formula:

$\displaystyle \frac{ - b}{2(- 1)} = - 7$

simplify multiplication:

$\displaystyle \frac{ - b}{ - 2} = - 7$

cross multiplication:

$\displaystyle - b = 14$

divide both sides by -1:

$\displaystyle b = - 14$

now we need to figure out C to do so substitute -7 for x and -5 for y which yields:

$\displaystyle - {7}^{2} - 14( - 7) + c = - 5$

simplify square:

$\displaystyle -49 - 14( - 7) + c = - 5$

simplify multiplication:

$\displaystyle -49 + 98+ c = - 5$

simplify addition:

$\displaystyle 49+ c = - 5$

cancel 49 from both sides:

$\displaystyle c = - 54$

hence,

• b=-14
• C=-54

Answer 2

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Problem:

• Find the unknown values of b and c in the equation y = -x² + bx + c given its vertex is (-7, -5).

Let's Solve it!

• This is a problem where you want to able to ake use of tue Vertex Form in order to get the values of b and c fir the standard form of the parabola. Vertex (-7,-5) or (h,k) in the standard form. These are the x and y coordinates of the vertex.

Note the standard form is:

$\quad\quad\quad\quad\tt{ a{x}^{2} + bx + c}$

Since we have the given of:

$\quad\quad\quad\quad\tt{ a \: = - 1}$

$\quad\quad\quad\quad\tt{ h = - 7}$

$\quad\quad\quad\quad\tt{ k \: = - 5}$

Note the vertex form is:

$\quad\quad\quad\quad\tt{y = a(x - h {)}^{2} } + k$

$\quad\quad\quad\quad\tt{y = - 1(x - ( - 7) {)}^{2} } + ( - 5)$

$\quad\quad\quad\quad\tt{y = - 1(x + 7 {)}^{2} } - 5$

$\quad\quad\quad\quad\tt{ \boxed{y = - {x}^{2} - 14x - 54}}$

Hence, The answer for b and c is:

$\quad\quad\quad\quad\tt{ \boxed{ \boxed{ \color{magenta}{b = - 14}}}}$

$\quad\quad\quad\quad\tt{ \boxed{ \boxed{ \color{magenta}{c = - 54}}}}$

Let's confirm it :

• You can use x coordinate of the vertex like this,

$\quad\quad\quad\quad\tt{ - 7 = \frac{b}{2(a)} }$

$\quad\quad\quad\quad\tt{ - 7 = \frac{b}{2(-1)} }$

$\quad\quad\quad\quad\tt{ - 7 = \frac{b}{-2} }$

$\quad\quad\quad\quad\tt{ (- 2)( - 7) = - b }$

$\quad\quad\quad\quad\tt{ \frac{ (- 2)( - 7)}{ - 1} = b }$

$\quad\quad\quad\quad\tt{ \frac{ 14}{ - 1} = b }$

$\quad\quad\quad\quad\tt{ \boxed{ - 14 = b }}$

• You can also confirm the y coordinate of the vertex in the standard form by plugging the x coordinate.

$\quad\quad\quad\quad\tt{y = - {(-7)}^{2} - 14(-7) - 54}$

$\quad\quad\quad\quad\tt{y = - 49 +98 - 54}$

$\quad\quad\quad\quad\tt{y = - 49 +98 - 54}$

$\quad\quad\quad\quad\tt{y = 49 - 54}$

$\quad\quad\quad\quad\tt{ \boxed{y = - 5}}$

So, the final answer for b and c is:

$\quad\quad\quad\quad\tt\huge{ \boxed{ \boxed{ \color{magenta}{b = - 14}}}}$

$\quad\quad\quad\quad\tt\huge{ \boxed{ \boxed{ \color{magenta}{c = - 54}}}}$

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✍︎ C.Rose❀