Properties of Quadratic functions
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1 Name Today s Learning Goals: #1 How do we determine the axis of symmetry and vertex of a quadratic function? Properties of Quadratic functions Date 5-1 Properties of a Quadratic Function A quadratic equation is an equation in the form of y= ax 2 + bx + c, where the highest degree is 2. The graph of a quadratic equation is called a parabola. In mathematics, a parabola is a plane curve which is symmetrical and is approximately U-shaped. The parabolas either open or. The turning point of the parabola is called the. The vertex can either be a or value. The vertical line that cuts the parabola into two equal halves is called the. The axis of symmetry always passes through the of the parabola. DIRECTIONS: Based on the definitions above, label the vertex, axis of symmetry, x-intercepts, and y-intercept of the parabola below.
2 FINDING THE PROPERTIES OF A PARABOLA WHEN GIVEN THE GRAPH For each of the parabolas graphed below, please find the following: a. The equation of the axis of symmetry b. The coordinates of the vertex c. The coordinates of the y-intercept
3 FINDING THE Y-INTERCEPT WHEN GIVEN THE EQUATION What is the y-intercept of a graph? How can you find the coordinates of the y-intercept when given the equation of a parabola? 1. Consider the quadratic function f(x) = 3 + 4x x 2. (a) Find the coordinates of the y-intercept of the graph of f. 2. The graph of the quadratic function f(x) = (x 5)(x + 1) intersects the y-axis at point A. (a) Find the coordinates of point A.
4 FINDING THE AXIS OF SYMMETRY AND VERTEX WHEN GIVEN THE EQUATION The axis of symmetry is the vertical line that cuts the parabola into two equal halves. To find the axis of symmetry, you can use the axis of symmetry formula that is given to you in the IB Formula Booklet. Before you use the axis of symmetry formula, first make sure the quadratic equation is expressed in standard form. The axis of symmetry always passes through the vertex of a parabola. This means that the axis of symmetry is always the x-value of the coordinates of the vertex. 3. Consider the quadratic function f(x) = x 2 + 4x + 5. (b) State the coordinates of the vertex.
5 4. Consider the quadratic function f(x) = 3 + 4x x 2. (b) State the coordinates of the vertex. 5. The graph of the quadratic function f(x) = x 2x 2 has its vertex at point B. (a) Find the coordinates of B.
6 PUTTING IT ALL TOGETHER 6. The graph of the quadratic function f(x) = 5 12x 2x 2 intersects the y-axis at point A and has its vertex at point B. (b) Find the coordinates of B. (c) Find the coordinates of A.
7 Name Date 5-1 Homework 1. For each of the parabolas graphed below, please find the following: The equation of the axis of symmetry The coordinates of the vertex The coordinates of the y-intercept a) b) c)
8 2. Consider the quadratic function f(x) = 6 + x x 2. (a) Find the coordinates of the y-intercept of the graph of f. 3. Consider the quadratic function f(x) = 10x + 2x 2. (b) State the coordinates of the vertex. 4. The graph of the quadratic function f(x) = x 4x 2 intersects the y-axis at point A and has its vertex at point B. (b) Find the coordinates of B. (c) Find the coordinates of A.
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