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For the following quadratic equation, find the discriminant.

-6x^(2)-8x+29=-7x^(2)-4
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $-6 x^{2}-8 x+29=-7 x^{2}-4$ $\newline$ Answer:

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Transformations of functions

Full solution

Q. For the following quadratic equation, find the discriminant.

\newline

-6 x^{2}-8 x+29=-7 x^{2}-4

\newline

Answer:

Bring to Standard Form: First, we need to bring the quadratic equation to standard form, which is $ax^2 + bx + c = 0$ . The given equation is $-6x^2 - 8x + 29 = -7x^2 - 4$ . Let's move all terms to one side to get it into standard form.
Isolate Zero: Add $7x^2$ to both sides and add $4$ to both sides to isolate the zero on the right side of the equation: $\newline$ $-6x^2 + 7x^2 - 8x + 29 + 4 = 0$
Combine Like Terms: Combine like terms to simplify the equation: $\newline$ $x^2 - 8x + 33 = 0$ $\newline$ Now we have the quadratic equation in standard form, where $a = 1$ , $b = -8$ , and $c = 33$ .
Calculate Discriminant: The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by the formula $D = b^2 - 4ac$ . Let's calculate the discriminant using the values of $a$ , $b$ , and $c$ we found.
Substitute Values: Substitute $a = 1$ , $b = -8$ , and $c = 33$ into the discriminant formula: $\newline$ $D = (-8)^2 - 4(1)(33)$
Calculate Result: Calculate the discriminant: $\newline$ $D = 64 - 4(33)$ $\newline$ $D = 64 - 132$ $\newline$ $D = -68$

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\text{}(B)g(x) = 9|x-2| - 4\text{]}

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\text{}(C)g(x)=-9|x-2| +4\text{]}

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\text{(D)}g(x) = -9|x + 2| + 4\text{]}

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