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Find all zeros of the functions below. 25 • h(x) = x² - 4x + q(x) = 3r²+ 23x 14. - Respond in the space provided.

Find all zeros of the functions below. 25 • h(x) = x² - 4x + q(x) = 3r²+ 23x 14. - Respond in the space provided.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Finding Zeros of Quadratic Functions In this section, we will find all zeros of the given quadratic functions. The zeros of a function \( f(x) \) are the values of \( x \) that make \( f(x) = 0 \). #### Functions to Consider 1. \( h(x) = x^2 - 4x + \frac{25}{4} \) 2. \( q(x) = -3x^2 + 23x - 14 \) Please respond with the steps and calculations in the space provided below. #### Steps to Solve For each function, follow these steps: 1. **Set the function equal to zero:** - \( h(x) = 0 \) ⟹ \( x^2 - 4x + \frac{25}{4} = 0 \) - \( q(x) = 0 \) ⟹ \( -3x^2 + 23x - 14 = 0 \) 2. **Solve the equation for x:** - Use the quadratic formula \( x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a} \), where \( a \), \( b \), and \( c \) are coefficients from the quadratic equation \( ax^2 + bx + c = 0 \). ***Note:*** For the detailed explanation, it is vital to show your work step-by-step in the blank space provided. --- Respond in the space provided below.
Transcribed Image Text:### Finding Zeros of Quadratic Functions In this section, we will find all zeros of the given quadratic functions. The zeros of a function \( f(x) \) are the values of \( x \) that make \( f(x) = 0 \). #### Functions to Consider 1. \( h(x) = x^2 - 4x + \frac{25}{4} \) 2. \( q(x) = -3x^2 + 23x - 14 \) Please respond with the steps and calculations in the space provided below. #### Steps to Solve For each function, follow these steps: 1. **Set the function equal to zero:** - \( h(x) = 0 \) ⟹ \( x^2 - 4x + \frac{25}{4} = 0 \) - \( q(x) = 0 \) ⟹ \( -3x^2 + 23x - 14 = 0 \) 2. **Solve the equation for x:** - Use the quadratic formula \( x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a} \), where \( a \), \( b \), and \( c \) are coefficients from the quadratic equation \( ax^2 + bx + c = 0 \). ***Note:*** For the detailed explanation, it is vital to show your work step-by-step in the blank space provided. --- Respond in the space provided below.
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