Solving Quadratic Equations: Methods and Practice
"Learn how to solve quadratic equations using graphing and algebraic methods, with real-life problem-solving examples. Explore factorization and root finding in this comprehensive guide."
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Presentation Transcript
Bellwork The volcanic cinder cone PuuPuai in Hawaii was formed in 1959 when a massive lava fountain erupted in Kilauea Iki Crater, shooting lava hundreds of feet into the air. When the eruption was most intense, the height h (in feet) of the lava t seconds after being ejected from the ground could be modeled by ? ? = ????+360t 1.How high is the lava after 7 seconds? 2.Determine when the lava will be 1400 feet in the air. 3.What is the vertex of the function? Explain what the vertex represents? 4.Over what time interval is the height of the lava increasing? 5. Over what time interval is the height of the lava decreasing? 6. How long is the lava in the air?
Bellwork Factor the trinomials: 1. ??+ ?? + ? 2. 2. ?? ?? + ? 3. 3. ??? ??? + ?? 4. 4. ???+ ?? ??
Bellwork Factor the trinomials: 1. -6??+ ??? ? 2. 2. ??+ ?? ?? Solve the equations: 1. 1. ??? ? = ?? 2. 2. ???= ?? + ?
Solving Quadratic Equations Section 3.1
What You Will Learn Solve quadratic equations by graphing. Solve quadratic equations algebraically. Solve real-life problems.
Solving Quadratic Equations by Graphing A quadratic equation in one variable is an equation that can be written in the standard form, where a, b, and c are real numbers and a 0. ???+ ?? + ? = ? A root of an equation is a solution of the equation. You can use various methods to solve quadratic equations.
Solving Quadratic Equations by Graphing
Solving Quadratic Equations by Graphing
Solving Quadratic Equations Using Square Roots
Take Note You know the x-intercepts of the graph of f(x) = a(x p)(x q) are p and q. Because the value of the function is zero when x = p and when x = q, the numbers p and q are also called zeros of the function. A zero of a function f is an x-value for which f(x) = 0.
Finding the Zeros of a Quadratic Function Find the zeros of f (x) = 2?? 11? + 12.
