Math Problem Statement
Solution
You have provided an image with the title "Gambarlah Grafik Fungsi Kuadrat di bawah ini," which translates to "Draw the Graph of the Quadratic Functions below." There are five quadratic inequalities or equations listed. Let's go through each of them.
1.
This is a quadratic inequality. To solve this:
- First, solve the quadratic equation to find the critical points.
- Then determine the intervals where the inequality holds true by testing values in each interval.
2.
This inequality involves finding the roots of and then testing intervals for .
3.
Similar process: solve to find the roots, then determine where the inequality holds.
4.
This is a simple quadratic equation. Find the roots of the equation to plot the parabola.
5.
Here, solve , and determine where the quadratic expression is greater than zero.
If you'd like, I can solve any specific one of these, graph them, or provide more details. Would you like to start with solving one of these?
Here are some questions related to these inequalities:
- How do you find the critical points of a quadratic inequality?
- What does the graph of a quadratic function look like?
- How do we determine the intervals where a quadratic inequality holds true?
- Can you explain how the discriminant helps in understanding the nature of roots?
- What are the steps for graphing quadratic inequalities?
Tip: The sign of the leading coefficient in a quadratic function determines whether the parabola opens upwards or downwards.
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Math Problem Analysis
Mathematical Concepts
Quadratic Inequalities
Quadratic Equations
Algebra
Formulas
General form of quadratic equations: ax^2 + bx + c = 0
Solving quadratic inequalities using factorization or quadratic formula
Theorems
Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a
Discriminant to determine the nature of the roots: Δ = b^2 - 4ac
Suitable Grade Level
Grades 9-12