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What is the discriminant of the quadratic equation
4x^(2)-3x-5=0 ?

-71

-89
89
71

What is the discriminant of the quadratic equation $4 x^{2}-3 x-5=0$ ? $\newline$ $-71$ $\newline$ $-89$ $\newline$ $89$ $\newline$ $71$

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Transformations of functions

Full solution

Q. What is the discriminant of the quadratic equation

4 x^{2}-3 x-5=0

?

\newline

-71

\newline

-89

\newline

89

\newline

71

Identify Coefficients: The discriminant of a quadratic equation in the form $ax^2 + bx + c = 0$ is given by the formula $D = b^2 - 4ac$ . We need to identify the coefficients $a$ , $b$ , and $c$ from the given equation and then apply the formula.
Given Quadratic Equation: The given quadratic equation is $4x^2 - 3x - 5 = 0$ . Here, the coefficient $a$ is $4$ , the coefficient $b$ is $-3$ , and the coefficient $c$ is $-5$ .
Calculate Discriminant: Now we will calculate the discriminant using the formula $D = b^2 - 4ac$ . Substituting the values of $a$ , $b$ , and $c$ , we get $D = (-3)^2 - 4(4)(-5)$ .
Final Result: Calculating the discriminant, we have $D = 9 - 4(4)(-5) = 9 - (-80) = 9 + 80 = 89$ .

More problems from Transformations of functions

Question

g(x)

g(x)

is the reflection across the x-axis of

f(x)=9|x+2|-4

\newline

\newline

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

\newline

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

\newline

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

\newline

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

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What does the transformation

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\newline

\text{translates it } 4 \text{ units right}

\newline

\text{translates it } 4 \text{ units down}

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\text{translates it } 4 \text{ units up}

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What does the transformation

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\newline

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[A] stretches it vertically

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[B] stretches it horizontally

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[C]shrinks it horizontally

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[D]shrinks it vertically

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\newline

\newline

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\newline

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\newline

g(x) = 10x + 17

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Question

What kind of transformation converts the graph of

f(x) = -3x^2 - 4

into the graph of

g(x) = -3x^2 + 6

\newline

\newline

\text{[A]translation 10 units up}

\newline

\text{[B]translation 10 units down}

\newline

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\text{[D]translation 10 units right}

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Question

y=x^{2}

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. What is the equation of the new parabola?

\newline

y=

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Question

y=x^{2}

is shifted down by

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units and to the right by

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\newline

What is the equation of the new parabola?

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y=x^{2}

is shifted up by

2

units and to the right by

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What is the equation of the new parabola?

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Question

y=x^{2}

is reflected across the

x

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\newline

What is the equation of the new parabola?

\newline

y=\square

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Question

y=x^{2}

is scaled vertically by a factor of

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\newline

What is the equation of the new parabola?

\newline

y=

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Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant