Mathematics 9 Lesson 3: Quadratic Functions
Download as PPTX, PDF11 likes7,762 views
Quadratic functions are polynomial equations of the form f(x) = ax² + bx + c, with specific characteristics based on the value of 'a'. The document explains how to graph a parabola by determining its vertex, axis of symmetry, and intercepts, as well as how to represent the function in vertex form. Essential steps for graphing include finding the vertex, creating a table of values, and plotting points to connect with a smooth curve.
1 of 14
Downloaded 323 times
More Related Content
What's hot (20)
Ad
Viewers also liked (20)
Ad
Similar to Mathematics 9 Lesson 3: Quadratic Functions (20)
More from Juan Miguel Palero (20)
Recently uploaded (20)
Mathematics 9 Lesson 3: Quadratic Functions
- 2. QUADRATIC FUNCTION It is a second degree polynomial Equation: f(x) = ax2 + bx + c where a, b, and c are real numbers
- 3. QUADRATIC FUNCTION Vertex Form Equation: f(x) = a(x – h)2 + k where, a ≠ 0
- 4. QUADRATIC FUNCTION Parabola • It is the graph of the quadratic equation
- 5. QUADRATIC FUNCTION If a > 0, the parabola opens upward If a < 0, the parabola opens downward
- 8. y = a(x-h)2 + k Vertex: (h,k) Axis of Symmetry: x = h
- 9. GRAPHING A PARABOLA WITH EQUATION IN VERTEX FORM To graph f(x) = a(x-h)2 + k 1. Determine whether the parabola opens upward or downward. If a > 0, it opens upward. If a < 0, it opens downward 2. Determine the vertex of the parabola. The vertex is (h, k)
- 10. GRAPHING A PARABOLA WITH EQUATION IN VERTEX FORM 3. Find any x-intercept by replacing f(x) with 0. Solve the resulting quadratic equation for x. 4. Find the y-intercept by replacing x with 0. Solve the resulting equation for y. 5. Plot the intercepts and vertex. Connect these points with a smooth curve
- 11. GRAPHING QUADRATIC FUNCTIONS 1. Determine the coordinates of the vertex by finding the x-coordinate from the formula x = − b 2a . Substitute the x-coordinate into the original quadratic function, and solve for y to determine the y-coordinate for the vertex
- 12. GRAPHING QUADRATIC FUNCTIONS 2. Determine a table of values by choosing at least two x-values that are greater than the x- coordinate of the vertex and two corresponding x- values that are less than the x-coordinate of the vertex
- 13. GRAPHING QUADRATIC FUNCTIONS 3. Graph the function by plotting the vertex and the set of ordered pairs from the table of values. Next, connect the points with a smooth curve.