5.2.2 – Intercept Form.

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Presentation transcript:

5.2.2 – Intercept Form

We have covered two forms of quadratics; Standard Form; y = ax2 + bx + c Vertex Form; y = a(x – h)2 + k The third will also us to find two specific points on the graph, if they exist

Intercept Form Recall, the x-intercepts are the points a graph crosses the x-axis Intercept Form is expressed as; y = a(x – p)(x – q), where p and q are the x-intercepts

Be careful! Similar to the vertex form of a parabola, we must think opposite when it comes to finding the intercept values So, if shown y = a(x – 4)(x + 3), the intercepts are x = 4 and x = -3, not the opposite

Example. Determine the x intercepts for the following equations A) y = 2(x – 3)(x – 5) B) y = (x + 9)(x – 3) C) y = -9(x + 4)(x) D) y = 4(x – 5)2

Graphing Using the intercepts, we will be given two of the three points we need What is the third point we will need? Vertex; x = (p + q)/2, then plug back in to get the y-value

Example. Graph the following equation Example. Graph the following equation. Label the vertex and y-intercepts. y = (x – 3)(x – 7)

Example. Graph the following equation Example. Graph the following equation. Label the vertex and y-intercepts. y = 2(x + 4)(x – 4)

Example. Graph the following equation Example. Graph the following equation. Label the vertex and y-intercepts. y = -2(x + 1)(x – 3)

Assignment Pg. 231 13-21, 28-30, 44-50 even Due MONDAY Quiz tomorrow!

Working together, find the graphs for the following equations; 1) y = (x – 2)(x + 6) 2) y = -(x – 3)(x – 6) 3) y = 3(x + 3)(x – 1) We will go over the assignment together afterwards.