Given $h(t) = -2(t+5)^2 + 4$, Find $h(-8)$.A. − 334 -334 − 334 B. − 14 -14 − 14 C. 45 45 45 D. 445 445 445

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Introduction

Quadratic functions are a fundamental concept in mathematics, and they have numerous applications in various fields, including physics, engineering, and economics. In this article, we will focus on finding the value of a quadratic function at a given point. We will use the given function $h(t) = -2(t+5)^2 + 4$ to find the value of $h(-8)$.

Understanding the Quadratic Function

The given function $h(t) = -2(t+5)^2 + 4$ is a quadratic function in the form of $f(x) = ax^2 + bx + c$. In this case, the coefficient of the squared term is $-2$, the coefficient of the linear term is $0$, and the constant term is $4$. The function is also in the form of $f(x) = a(x-h)^2 + k$, where $(h,k)$ is the vertex of the parabola.

Finding the Value of the Function at a Given Point

To find the value of the function at a given point, we need to substitute the value of the point into the function. In this case, we need to find the value of $h(-8)$.

Substituting the Value of the Point into the Function

To find the value of $h(-8)$, we need to substitute $t = -8$ into the function $h(t) = -2(t+5)^2 + 4$. This gives us:

h(−8)=−2(−8+5)2+4h(-8) = -2(-8+5)^2 + 4

Evaluating the Expression

To evaluate the expression, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the parentheses: $-8+5 = -3$
  2. Square the result: $(-3)^2 = 9$
  3. Multiply the result by $-2$: $-2(9) = -18$
  4. Add $4$ to the result: $-18 + 4 = -14$

Conclusion

Therefore, the value of $h(-8)$ is $-14$.

Final Answer

The final answer is B. −14-14.

Introduction

Quadratic functions are a fundamental concept in mathematics, and they have numerous applications in various fields, including physics, engineering, and economics. In our previous article, we discussed how to find the value of a quadratic function at a given point. In this article, we will provide a Q&A section to help you better understand quadratic functions and how to work with them.

Q&A: Finding Values of Quadratic Functions

Q: What is the value of $h(t) = -2(t+5)^2 + 4$ at $t = -8$?

A: To find the value of $h(-8)$, we need to substitute $t = -8$ into the function $h(t) = -2(t+5)^2 + 4$. This gives us:

h(−8)=−2(−8+5)2+4h(-8) = -2(-8+5)^2 + 4

Evaluating the expression, we get:

h(−8)=−2(−3)2+4h(-8) = -2(-3)^2 + 4

h(−8)=−2(9)+4h(-8) = -2(9) + 4

h(−8)=−18+4h(-8) = -18 + 4

h(−8)=−14h(-8) = -14

Q: What is the vertex of the parabola represented by the function $f(x) = ax^2 + bx + c$?

A: The vertex of the parabola represented by the function $f(x) = ax^2 + bx + c$ is given by the formula:

h=−b2ah = -\frac{b}{2a}

Q: How do I find the x-intercepts of a quadratic function?

A: To find the x-intercepts of a quadratic function, we need to set the function equal to zero and solve for x. This can be done using the quadratic formula:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Q: What is the difference between a quadratic function and a linear function?

A: A quadratic function is a function of the form $f(x) = ax^2 + bx + c$, where $a$ is not equal to zero. A linear function, on the other hand, is a function of the form $f(x) = mx + b$, where $m$ is not equal to zero.

Q: Can a quadratic function have more than one x-intercept?

A: Yes, a quadratic function can have more than one x-intercept. This occurs when the discriminant ($b^2 - 4ac$) is positive.

Q: How do I determine the direction of the parabola represented by a quadratic function?

A: To determine the direction of the parabola represented by a quadratic function, we need to look at the coefficient of the squared term ($a$). If $a$ is positive, the parabola opens upward. If $a$ is negative, the parabola opens downward.

Conclusion

In this article, we provided a Q&A section to help you better understand quadratic functions and how to work with them. We discussed how to find the value of a quadratic function at a given point, how to find the vertex of the parabola, how to find the x-intercepts, and how to determine the direction of the parabola. We hope this article has been helpful in your understanding of quadratic functions.

Final Answer

The final answer is B. −14-14.