Algebra 1: Graphing Quadratics Quiz

Vertex of Quadratic Functions

• Vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) is the vertex.
• The vertex is the highest or lowest point of the parabola, depending on the value of 'a'.
• For y = 3(x - 9)^2 + 1, the vertex is (9, 1).
• For y = -1(x + 9)^2 - 1, the vertex is (-9, -1).
• For y = 4(x + 7)^2 + 8, the vertex is (-7, 8).
• For y = -4(x + 8)^2 - 7, the vertex is (-8, -7).
• For y = 2(x - 3)^2 + 5, the vertex is (3, 5).
• For y = (x + 6)^2 - 2, the vertex is (-6, -2).
• For quadratic in standard form y = x^2 + 6x - 1, the vertex can also be found at (-3, -10).
• For y = x^2 - 4x + 3, the vertex is (2, -1).
• For y = 2x^2 + 4x - 10, the vertex is (-1, -12).
• For y = 3x^2 - 6x + 8, the vertex is (1, 5).

Y-Intercept of Quadratic Functions

• The y-intercept is found by evaluating the function at x = 0.
• For y = 5x^2 - 6x + 10, the y-intercept is 10.
• For y = x^2 + 4x + 8, the y-intercept is 8.
• For y = 3x^2 + 6x - 1, the y-intercept is -1.
• For y = 2(x + 1)^2 - 4, the y-intercept is -2.
• For y = -3(x - 4)^2 + 8, the y-intercept is -40.

X-Intercepts & Roots of Quadratic Functions

• X-intercepts are found where y = 0, which gives the roots of the quadratic.
• For y = x^2 + 7x + 10, the roots are -7 and -2.
• For y = x^2 + 9x - 10, the roots are -10 and 1.
• For y = x^2 - 7x + 12, the roots are 4 and 3.
• For y = x^2 - 8x - 20, the solutions are 10 and -2.

Orientation of Parabolas

• A quadratic opens upwards if 'a' is positive and downwards if 'a' is negative.
• For y = -4(x + 5)^2 + 10, the parabola opens down.
• For y = 3x^2 + 9x - 1, the parabola opens up.